Thanks for your question and concern. It is a difficult thing to understand who the parent by you is. But it sounds like the paternity test could easily help you. The main test involve in a paternity testing is to take a blood sample or the DNA sample from one or both the potential fathers and test it. The result will prove who the father is? So it would be a hard job for you to talk to each of them about your current situation you are facing.
If you are doing the paternity test, then the test result should be done as early as the 10th week of the pregnancy period. In the NHS you would not get the test as it is a payable service. Even the test is a court directed one then also you should have to pay for the test. Court directed tests are done for getting the maintenance support to the child. The only time you should not have to pay is during the time of getting the government help for the fees.
If you would like to get more information or any other type of data then you should visit your personal or nearest doctor (GP). He will help in getting advice for your doubts. Take care