A doctor can't 'lie' about a diagnosis. What would the purpose be? To sell some antibiotics? He can lose his license for an offense like that, so I doubt that was what happened. Besides, how much did the antibiotics cost? Not very much in the big scheme of things, that is for sure.
If your boyfriend has chlamydia and you don't, but you've had a relationship where you were active without condoms until recently (when he moved), I think you know the answer yourself. If he'd had chlamydia in the past, he'd have given it to you. Especially if you were having a sexual relationship without condoms for 3 years.
You can not get chlamydia from a towel or a toilet seat. It is called a 'sexually transmitted' disease for a reason. It is transmitted sexually.