Your voice does not totally suck, there are definitely worse people in the music program at my university, but that doesn't mean you don't need further training to be great.
I took private voice for a semester, and I don't really think it helped much. I probably should have put in more proper practice outside of class, but it was a really busy semester.
Two things really helped me: the beginning voice class I took at my university before private voice, and being in a choir, which I did after private voice. The beginning voice class gave me more of an idea of what I actually needed to be working on, and the choir met 4 days a week, so I was forced to do warm ups and sing with people on a regular basis.
I was also going to suggest you have a look at the "Singing Success" channel on YouTube, but it looks like they now also have video and such on their own website: . They really just want to sell you some CD sets about singing, but they have plenty of helpful information in their free videos too.
I have one last piece of advice. When you see people sing live, watch everything about their technique: their posture, breathing, how wide their mouths are open, etc. That stuff is really important.