I'm probably not going to make any friends with this post, but I want to be real with you. Reading your OP, I have a number of concerns here.
Eight withdrawls
is a lot. Are these all in science/pre-req courses? If so, then I feel like that's going to impact your application more negatively than if they weren't, especially because you indicated that these withdrawals are all littered throughout your undergraduate career, and not just at the beginning or during one particularly difficult semester/year.
A 3.3 cumulative GPA is definitely not the end of the world, particularly if you apply to schools which either do not look at cumulative GPA or weigh it less heavily than last 45 and science GPAs (ie. Iowa State, Kansas State). That said, you didn't tell us how your other GPAs look, which is going to make a
huge difference as to whether or not you'll still be competitive. For instance, I personally had a 3.21 cumulative GPA when I applied and was accepted to 3/4 of the vet schools I applied to... the kicker, though? I had a 3.7 science GPA and nearly a 3.8 last 45 hours GPA. If all of your GPAs (cumulative, science, last 45 hours) are at or around that 3.3 figure, you're going to have a much more difficult time getting into vet school than if you had a very strong upward trend and/or did very well in the vet school pre-reqs. Again, we can't know exactly how badly your chances are going to be impacted without the full picture and all of your stats.
@EngrSC addressed this a little bit already in her post, so I'm won't be too much of a broken record here, but you mentioned that you've been going to school mostly part-time---were you also working full-time while you went to school? If not, this may lose you some points with certain schools, such as Mizzou and UTK, which award points based upon average courseload.
Full disclaimer, of course, that I'm not an adcomm, but simply based upon what's in this post---without knowing how your entire application, including veterinary/animal/work experience, looks---I don't know that I'd be convinced that you'd make it through a DVM program. As someone who also has had a very severe mental health history, including generalized anxiety and bipolar II disorder, I can somewhat empathize with what you're dealing with... but I'm also not going to lie to you: vet school is difficult and exhausting, to the point that it often unmasks mental illness in those who may not have had those struggles prior. It is especially incredibly hard on those who already have a history of mental illness going into it. This isn't to say that you can't make it through with anxiety or depression or ADHD or another psychological condition---people have done so and you certainly can, too---but it is
imperative that you have a solid treatment plan and adaquete support system in place, whether that be in the form of medication, therapy, lifestyle changes, or a combination of some or all of those things. If you do not, you may be signing yourself up for a lot of headache and heartbreak; once vet school gets going, it doesn't really ever let up, so by the time you are drowning and really need the help, if you don't already have something in place, it may be too late to be saved.
I've posted about this many times in the past, albeit not recently, so you may not have seen me talking about it, but I more or less failed (I didn't actually fail any courses, but my GPA fell below the minimum standard to remain in good standing) out of vet school in my second year. Nearly halfway through the program. My mental health state had deteriorated to the point that, although I'd force myself to study nearly every waking hour outside of school, I'd retain little to none of it. And it really, really showed on exams. I wound up on academic probation after first year and basically was told that I needed to get my **** together during the fall of second year or that I would be dismissed. I tried, I really did... but I didn't manage to pull it off, leaving me without an income (couldn't get the rest of my loans for that year, wasn't allowed to keep my student jobs at the school) and having to move back in with my parents for nearly two years. I
just managed to snag a job that pays me well enough to actually live independently again.
I don't want this to happen to you. It's a horrible experience, and one that I could have avoided had I asked for help prior to the absolute precipice.
The reason why the number of withdrawals concerns me is that, in tandem with the bit about your struggles with anxiety, it has me worried that you start to consider withdrawing from courses once the going gets tough and you realize that you might do poorly in them. This is problematic for a couple of reasons. First, it tells me that you're not doing well in many of these courses to begin with and, as I mentioned above, if it's happening in science/pre-req courses, it's an especially bad sign because vet school is nothing more than hard science from 8-5 every single day. Second,
you cannot withdraw from individual courses in vet school, with the possible exception to that rule being electives. At least with the core curriculum courses in vet school, it's all or nothing. If you withdraw or otherwise take a leave of absence, you effectively put yourself behind at least a year by default. If your only way to tread water academically is to withdraw from courses you're not doing well in, that will no longer be an option in vet school.
I know this sounds really bleak, but I think it might still salvagable if you can get your anxiety under control (if you haven't already done this) and retake any courses you obtained a C or lower in. Yes, a C is technically still considered to be "good enough" by vet schools for a pre-req grade, but it still drags your GPA down. Alternatively, you could look into doing a masters or post-bacc program, if you are confident that you can do well, and it would certainly provide evidence to schools that you've overcome past struggles and can perform academically. Of course, utilizing the Explanation Statement on VMCAS is also certainly a great idea in this circumstance.
I feel like asking "How many withdrawals on a transcript are too many?" is a fraught endeavor because it's so situational and the answer will depend a lot upon so many factors, such as the individual school(s) you're wanting to apply to, as well as what the rest of your stats and experience look like. Again, it's really difficult to fully analyze your particular situation without the details of your full application and everything you bring to the table, but, at least jumping off from what's in your post... I would agree that it's not the 3.3 cumulative GPA alone that is killing you. It's the combination of that and the sheer number of withdrawals. I commend you for pinning down your anxiety as a reason for past academic difficulties, but now the question becomes how do you intend/what have you done in the time since to address it so that you can succeed in vet school? What evidence can you provide adcomms to demonstrate that you can make it through the program?