Thank you for writing!
NOT getting treated for chlamydia is one of the causes of infertility so as long as you are getting properly treated, you should be ok. But twice in a year (with two guys or the same one?) isn't ok. Insist on a condom. If I had a dollar for every male I've heard claim to "be clean" I'd be a rich woman. Unless he took a test with you and had no sex until he showed you the result, you don't know at all that he's "clean". Men often have no or fewer symptoms with STI's (and there is no test for male HPV) so there is a lot of leeway here. He may easily have passed it to you - it's a very common infection.
Now, he needs to be treated, regardless (as do you), even if he has no symptoms.