R.M.
My sister took lavanox her whole pregnancy then switched to heparin. She delievered right on schedule. Why are you concerned with preterm labor? Just because of the braxton hicks and you are wondering if they are related to the drugs? Are you saying that you have anxiety to explain that you might be just worrying about it due to the anxiety issues? I wouldn't worry if that is the case. If there is something else going on, you need to talk to your doctor. You can always call a pharmacist and ask if this is a risk associated with these drugs.
One thing to keep in mind- to my understanding you CAN NOT, absolutely can not, stop taking blood thinners once you are on them while pregnant. The risk of having a blood clot increases immensely if you are on them and get off. Are you currently taking them, or are you trying to decide whether to or not? If you are trying to decide, you need to have a conversation with your doctor about the risks of taking them, and the risks of not. Because if they are prescribing them for you there must be a very good reason to think you need them. They are not prescribed lightly. Good luck! I know this is a scary thing to deal with.