I agree with the suggestions to do one of the shorter routes. Even if you weren't currently having back pain, a century would hurt if your longest ride to date is 43 miles. Ideally, you want to have some rides under your belt in the 75-mile range before doing a century.
As for your back problems. If you've only been riding a couple of months, a 19.2 average over 33 miles is fabulous, but that kind of speed suggests to me that your back problems might relate to tight hamstrings. When I started doing speed work, my low back really bothered me. You might try stretching them before, during after your rides. If your low back still bothers you, you might see if bike fit is an issue.
Good luck and have fun!
Live with intention. Walk to the edge. Listen hard. Practice wellness. Play with abandon. Laugh. Choose with no regret. Continue to learn. Appreciate your friends. Do what you love. Live as if this is all there is.
--Mary Anne Radmacher