I'm assuming you're referring to a Cal State school, correct? If you're attending a California Community College, then yes you will need to transfer. If you're at a CSU, I would say transferring is a personal choice. You won't kill your medical school chances either way.
Re Cal States: There's huge variability across the CSU system, in regards to size, resources, and "perceived prestige." While CSUs are cheaper than UC schools, keep in mind that none have affiliated medical centers and most don't have huge pre-med pipelines (hence, less resources for premed students). I ended up having to seek out clinical opportunities from neighbouring UC schools, even though I was enrolled at a CSU. It turned out to be a bit of a pain, because I was blocked from participating in some really awesome programs they offered due to the fact that I wasn't a student there. I
would say that you have to be a far more proactive student at a CSU vs. a UC, because most CSU schools won't have as many well-established research/clinical programs. In fact, 90% of my application entries were non-CSU affiliated, since I had to search elsewhere to find the activities I wanted.
I'm not URM, but I attended a CSU whose student body was over 50% URM. What my school lacked in your typical pre-med resources, they made up for in awesome minority support programs. Our minority research support office had connections with a number of prestigious summer research programs and would set up a handful of URM students at Harvard/Baylor/UCLA/etc each summer. I bet this is very CSU-dependent, however.
Regarding the whole "perceived prestige" business, I couldn't say how much attending at low-tier CSU hurt me. Some med schools love to recruit from prestigious institutions, while others may be more forgiving. I've heard that some UC med schools will stick their nose up at CSU students, but I had a pretty good success rate with UC med schools. The one thing I had to deal with was constantly being questioned by interviewers as to why I went to a CSU vs. a UC school.
I can say that getting a high MCAT was instrumental in my success, as it "validated" the high GPA I got from my CSU. My prehealth counsellor insinuated that a not-well-known state school + low MCAT could be the kiss of death.
tl;dr: really, I would advise you to chose the school (within your financial range) that you feel you would be the happiest at. Whether you attend a podunk CSU or the top UC, you're going to want perform to your highest degree. Do well in your classes, get a good MCAT, and engage in activities you love. When all is said and done, the school is secondary. Good luck!