Hi there, i am no expert about this., but i just want to share some thoughts since i was in the same situation way back. Exact situation as what you're currently in right now, the only difference is that we're not yet living together. I know you're frustrated but don't take away the possibility that it could be your partner who is the carrier of the said infection. I'm also into reading medical websites and forums online and found out that you can't just get chlamydia through sexual intercourse (from other person) because there could be a possibility that the infection could be a mother-to-child transmission though that rarely happens.
I am not saying that either of you and your partner cheated if mother-to-child transmission doesn't apply to you both. What you could do best is to undergo treatment and do as what your doctor instructed. Good thing i have an open-minded boyfriend, he helped me go through to that one hell of experience. If you're partner truly loves you, he will also do the same and would still stick around. Just try to be open to him and bring him to the doctors with you. In that way, he will have the chance to know more about Chlamydia, the causes and the treatment.
Good luck and god bless..