Well you have a 3.5 GPA. Which is good. Are you a junior right now? Applying this summer? So you are graduating College next year? Or when? This matters because the farther away your graduation, the higher the chances of you taking on extra classes to offset those W's. Are you taking the MCAT this spring? Next winter/spring? Do you know anything about the MCAT? You should start practicing for it as soon as you get mentally well and feel like you are ready to get exposed to complete and utter hell (MCAT).
If you get a 3.7+ GPA BY THE TIME YOU APPLY, have a 34+ MCAT, have a very healthy amount of volunteering/clinical work/etc... then there is not a doubt in my mind you can make some allopathic school... somewhere. What is your state of residence? That matters a lot as well. Will you have good LOR? Is your therapist an MD/Psy.D/PhD? If your therapist is an MD (psychiatrist), then definitely share this dilemma with him/her.
Also, I was nice to you, so I figure now is an appropriate time to be stern. While I admire your persistence and determination, as someone who wants you to succeed (altruism does exist, eh?) please don't be hard-headed. You don't know a darn thing about neurosurgeons. Idc how many bifrontal temporal craniotomies you think you can perform, at the end of the day, you can't even fathom what it is like TO BE the man holding the scalpel. And no amount of Ben Carson youtube videos is going to change that.
I've seen neurosurgeries, and I worked at a cerebrovascular lab at a top hospital in the country, and I know from experience what it is like to be an academic neurosurgeon. Everything in your life will suffer. Your girlfriend/wife will most likely leave you. And if you ever have time to reproduce, your kids will never see you. You will only see your porsche after your 40th birthday, and even then, you'll only drive it to and from your work. The notion that neurosurgeons work 80 hours a week is also very understated. It is often much much more than that, and don't get me started about the residents. I was even more set on neurosurgery than you are.... but you know what, I always reserved the right to keep an open mind. (Since any surgical specialties are closer to being related to one another than their respective medical specialties, in my case, I view it differently. So for example, even though the jobs of a neurologist and a neurosurgeon couldn't be any farther apart, I would choose neurology over any other surgical specialty just because I want to stick with neurological pathologies. However most wanna-be surgeons who choose to switch specialties, will most likely switch into another surgical specialty. idk if this makes sense). What I am trying to say is that... be determined, but be humble, open minded, not aggressive, and not hard headed!
^ Feel free to answer the premed questions about your timeline, anticipated GPA, practice MCAT scores if any, state of residence, etc...