Could these be signs that im going to have a preterm baby?

Some of your symptoms sound completely normal while others would have me concerned. I would talk to your doctor more and make sure he knows everyone of the symptoms going on and have him check you to make sure everything is alright but if he says not to worry then you just have to trust him or get another opinion. Take it easy these next two months and get plenty of water and rest. I hope everything goes well!