I didn't do well my 1st year in community college, can I still transfer to a good university?

My first two semesters in community college, I didn’t do too well due to not liking my major, being distracted, not actually knowing what I wanted to do, being naive, and being put down a lot by counselors. I felt really lost. I got one D in psychology which isn’t required for my major now and I got a lot of C’s and some b’s and A’s. Last summer I took a refresher Biology course and fell in love, I absolutely admired my professor, and I decided I wanted to become a doctor and major in my undergrad in Biological Sciences. I’m actually really good in school which is why I was so shocked I was doing so poorly at first. So, this past fall(2016) I started my biology degree requirements and I’ve been doing well. Math has always been my weak spot and I need to get up to college level so I took elementary algebra which isn’t transferable and got an F 2016 fall but now I’m retaking it this semester and my new professor told me I will most likely finish with an A or a B. I am doing extremely well in all my classes and will finish this semester with A’s, my GPA right now is a 2.7 but I’m working on getting it higher. It is a lot easier now that I’m happier with my major.
Now that my plan is better and everything is more clear I would like to transfer to UCSD, USC, UCLA, or USD. I’ve talked to my counselor and she reluctantly told me that I would have to get A’s and B’s my next couple of years which I’m 100% sure I can do now as I am extremely passionate about my major but she is still very negative about my situation as are many other counselors I have talked to.
I’m wondering if there is anyone else that has been through this type of rough patch but came back from it, if so how did you do it? Any advice in general on how to get accepted to these schools as a transfer if I did bad at first?

Hey, I was in the same boat as you, however I didn’t apply to a university, I applied to a Cal State.

I did awful my first semester, I failed 3 of my classes and I didn’t care about college or anything, I just did it to make my parents happy. However, I decided to pick up the paste and do better than I did before and I exceeded my expectations. I was at a 2.7 GPA and I was worried that I wouldn’t get into CSULB, but once I applied they told me that I was in.

For advice – I would ask if there is a way to re-take the classes you did bad in, so the F’s don’t show? I had to do that, and it made my transcript look so much better.