Congrats on your dedication to get stronger on the bike!
You don't have to join a club to try out racing. There are several ways to get into the competitive side of the sport and several types of races. Team Revolution puts on a wonderful racing clinic each year but unfortunately it has already happened for 2013. (Even if you start racing this year, I'd recommend that you attend next year- usually in March- You'll learn a TON!).
I would encourage you to do some group rides and get comfortable riding close to others (if you haven't already). This will also give you a chance to talk about racing with girls who have some experience.
You can also try out time trials, which will give you a chance to work on speed without the mass-start. There is a Wednesday night Time Trial series (go to stltt.com for more info). Several of us "Team Rev" ladies attend the TT series -aka WNTT. Several new racers have started out here!
You can also try road races or criteriums (or track racing, but that's kind of a whole different animal!)
You will need a one day license for each race ($10) or purchase an annual license ($60) via usacycling.com. You will enter racing as a beginner - Category 4 (Men start out at Cat 5, Cat 4 is the equivalent for women).
Check out the calendar on stlbiking for upcoming races.
There are also training criteriums on Tuesdays, aka Tuesday night worlds (TNW's). The C race is for beginners, but that includes all beginners - men, women, juniors. There are some advantages and disadvantages to this. The training series races (TT or Crit) are only $10 each night (Plus your one day license if you don't buy an annual).
Most of the criteriums this year are Category 3/4 which means there are some more experienced racers in these races. That is both a strength and a challenge for new racers. Some of these races can be pretty fast (depending upon the course, the competitors and a myriad of other factors), but not everyone in that race goes that fast. Sometimes the races split up into a few groups of differing ability. While you may not win at a race like this, you'll still have fun and gain some valuable experience!
For most of us, our first race is a humbling experience. I'd encourage you to be open to trying anything twice. You can focus on just getting started in your first race and then hone your focus for a second one... then evaluate your goals
If you have more questions, posting here is a great place to start!