First, finish your degree...you don't want to start over at this point. I didn't decide to do PT until about Oct/Nov of my senior year, and I still managed to get in all the prereqs within one year of graduating (so I only had to take a year off). Like you, I had only taken psychology (and stats) prior to deciding to do PT, and my major was totally unrelated to the field.
Since you are in your third year, try to start taking classes that meet the prereqs if your schedule will allow it....if you're pretty close to completing the requirements for your major, you could feasibly get in all the prereqs before you graduate (especially if you took 2-3 classes in summer school at a community college between your junior and senior years). Worse case scenario, you may have to take a year off to take the extra classes you're missing. Either way, this would be much cheaper than trying to change your major now and/or start over and have to do at least 3-4 more years of undergrad.
And you can't specialize in anything until after you graduate from PT school...because of the licensing exam, all PT schools (at least that I'm aware of) have to have a general curriculum that prepares you to take the exam - no PT school will just teach you to be a pediatric PT, neuro PT, or ortho PT. It is my understanding that in order to be accredited, they must teach you to be a well rounded practitioner capable to practice in any setting. On the licensing exam there may be questions about wound care/burn management, as well as peds, neuro, ortho, and cardiopulmonary PT...if you've only been taught one thing, you won't pass the exam.
After graduation though, and when you work for a company, you can continue to take classes and get a specialization in pediatric PT, or neuro. Peds isn't going to only be paraplegic children though...you'll also get a lot of cerebral palsy, down syndrome, maybe some autism, etc. With neuro, you'll get some CP, but also a lot of stroke and spinal cord injury patients as well.
You'll also have to do some clinicals while in school, so you can try to get at least one of them in a pediatric setting, so that when you apply for a job after graduation you have some more experience in that arena.
Regardless, try to get some more shadowing experience, outside of the pediatric setting. Since you'll inevitably have to learn and do PT in other settings, make sure you at least somewhat enjoy the other settings too (you don't have to love it, but you don't want to hate it). Most PT schools require several shadowing experiences anyway.
Hope this helps...sorry it's so long. It turned into a novel. haha.