Birth before 37 weeks is a bit early. I don't think 37 weeks is premature (I believe it's called preterm) but anything before that is premature. Drs have become VERY adept at saving babies though and there are babies born at 28 weeks who survive! It's amazing. What I'm trying to say is...relax and IF you do go into labor your baby will most likely be fine! Maybe just a brief stay in the NICU...but medicine has come a long way
Make sure you are drinking A LOT of water (if you think you are having contractions drink/chug 30 Oz of water and go lay down on your left side). Other than that, I don't know what to tell you other than to go call your Dr or take a visit to the ER