I am so sorry for you that you have lost a child. The knowledge that there was another child who is no longer here is painful and I think you are right to explore it, try to deal with it and find a way to heal as best you can.
I am sorry that you had had such treatment during your early pregnancy and that neither doctors were fully open with what they saw or tested. There are many factors that could have been at play here and the risks should have been explained to you at the time.
There are antibiotics that are not recommended in pregnancy, that cause higher risk of miscarriage and folate antagonists do lead to a higher risk of miscarriage. In prescribing antibiotics that are not advised in pregnancy, doctors should ask patients of childbearing age if there is a possibility that they might be pregnant. I have been asked this on numerous occasions over the years.
It is not clear whether the second embryo had broken off before you started to take the antibiotics, whether an infection caused this or indeed, if there was some other reason for the miscarriage which was in fact the cause of the pain.
In an ideal situation, the first doctor would have discussed the urine test results with you and the possibility that you might be pregnant. He would have also explained the risks to your unborn child / children and in some cases the risks of the infection are greater than the risks of the treatment but the principles of informed consent should ensure that you have understood those risks. As others have pointed out, the first doctor may not have known you were pregnant, which make the comments of the second doctor odd at best. It is possible that the lab test results included an HCG test and that his subsequent comments were in shock at the unintentional mistake that had happened.
If you can, I would make an appointment with a doctor to discuss the events and your concerns. Insist that you understand that the events may have had no connection with the miscarriage but that it would help you to understand the chronology of events and that the comments at the time have been playing on your mind. You are never likely to know for sure what caused the loss of your child but you might be able to stop these thoughts going round in your head. Doctors do make mistakes and sometimes medications do cause unwanted effects. I would do this within the safety of counselling to support you through this, help you deal with the loss and the fact that you cannot have any more children.
Take care of yourself lovely lady.