At a certain point all of us, even those without BPD, have to decide whether to trust another person or not. I try to think of all the times the other person has told me the truth and the number of times they've lied. If you can think of 100 examples where he's told the truth and no examples of him lying, you might be in a place where you have to decide to trust him. The suspicious thoughts will still arise but through therapy you can learn to defuse those thoughts so that they have less power over you.

Medications can blunt the suspicious thoughts but they have lots of side effects and many will blunt all of your thoughts so I'm not sure it's a good route to take.