Academically Dismissed after my first year but have proof that it was my health problems

So My first year of college was Fall 2015 I was in a new relationship until everything when downhill a month and a half later I found out my boyfriend got my cousin pregnant after a night out of us partying and My life fell apart my grades started to drop I was so unfocused which dropped me back into depression, I had and still do have a mental health issue and history of depression and bipolar which my doctor knew about. The whole semester I passed only 2 classes out of 5 which was bad I was let of with a academic probation after Spring 2016 I dealt with the stress once again because now my family blamed me for this situation it got really bad and I fell once into my depression stage, with work and family problems I manage to pass all my classes but with a low GPA but I got a letter saying I got Dismissed it was truly disappointing but I wanted to file an appeal but I don’t know how to explain all of this. I want to be able to return in Spring 2017 but I wanted to transfer out will the classes I took be able to get transferred out?

There are a couple of issues here.
One is that it sounds like you want to try to change some Fs to Ws. You should contact the advising office for advice. You would have to submit information indicating that you have been diagnosed with depression. Ideally you would have been registered with the disabilities office (if you get back in, you might want to do that.)

The second issue is whether even after changing Fs to Ws if you would still be making academic progress given how few credits you would have earned. You might need to go to a school with open admissions (a community college) first. You would need to send them your transcripts from the first school.

I have seen a therapist but I also told him about my situation in school and he said he would give me a document regarding my diagnosis because it runs in my family. Would it be best going to my College Mental health Counselors explaining my situation, then meeting with my academic adviser with proof?

Meet with your academic advisor. That person will know the school policy and will be able to let you know what steps you need to take. Do you have a school handbook? It’s often in the catalog. Each school is different, but some allow for F-repeats (you take the course again, each grade remains on transcript but only passing grade is counted in GPA.)