As for me, I hope you don't mind me posting this but I had a little bonus scan today. Ducky is still alive and even kicked and waved at us, which was pretty incredible.
I think that if you had a clot in your womb whilst pregnant the last thing you should have is blood thinners. Any extra blood in there causes a higher risk of the baby miscarrying.
I am probably going to be a bit controversial on here and say that unless you have a clotting factor or APS there is no point in taking heparin. They have run trials on women with unexplained miscarriages where they gave them heparin just in case and it made no difference to the outcome.
Aspirin is slightly different since it works differently and crosses the placenta (heparin doesn't and that is why it isn't that terribly necessary early on - unless you have APS, I believe). Some women come up negative with all known clotting tests and then a TEG test shows they gp need aspirin.
Obviously, I'm not the best person to speak as I am taking progesterone and there is no evidence I need to take it.
I just wanted to say that if your doctor won't give you heparin or only gives it to you from bfp then please don't panic! That is standard practice and there is research behind it.