As CK said, I've started racing, only recently (May 27th) so my experience is really limited. But, I'll just be brutally honest, if you're saying your average speed is 13.5 mph, forget racing for now. No ifs, no buts, just put it way off into the distance. And here's why.
By using the last 5 years I've put in the miles to see me progress from about a 15.5mph (ish I think) average to now comfortably sitting solo at 20+ mph average, sitting in a paceline at 30+ mph. It took me to knock in anything up to 13500 miles in a year to get my fitness to here from where it was. Then a couple of folk said I really should try racing, as I might do ok. My Cat 4 license drops on the doormat, I'm booked into my first race, and I start some sprint training. I thought I was bike fit until I started intervals, how wrong I was. A few weeks to go and the course I'm racing on has some track practice sessions so I thought it would be great to get the experience of the circuit layout under my belt. Whoosh, we rattle around like no-ones business, all Cats, 2's 3's and 4's all together, it was fantastic. I think we averaged 26.5 mph. Come race day, my first ever race, Cat 4, excited like a kid at Christmas, revved myself up and got the job done. Ended up with a 4th place, 0.8 seconds off the win, averaged 25.5 mph I think it was. Had I entered and lined up on the startline of this small local race back in 2011 when I was riding at 15.5mph, I would of been spat out the back quicker than you could say iknewthiswasabadidea. I would of therefore just been riding around the track on my own, probably just getting in the way of the ones who are smashing it.
Entering
a race with the average speed you're talking about won't get you experience of racing. Put some decent miles in, build that fitness right up, then think about it. What you could try is GoRace. Have a look on the British Cycling site.
