There's a place for everyone. I threw at san jose state, thats the same san jose state that in one international competition in the late 60s would been beaten the soviet union, had it been its own nation. The NCAA program was a casualty of budget cuts 20 years before I enrolled. I joined the club team as a true freshman, was the top shot putter there at about 31' on day 1, was the top shot putter there at 35'1" when we went our separate ways after my "redshirt sophomore" season.
We'd go against jr colleges that had kids throwing 26', heck we had a kid that threw 27-28'. Sounds like you're probably quick enough to be beating me within a couple months with good instruction. Any all comers meet or jr college meet (a lot are open to individual athletes, at least around here) would probably fun, competitive, and non-overwhelming for you. If you're open to sharing where do you go to school now and what is their track situation?