Probably yes but not necessarily.
You need to accept that there is no way to know the answers you seek with certainty. The information you have now is all you will ever have. You need to make your own decision whether to give your husband the benefit of the doubt or not. I cannot help further.
If my husband had cleared the infection himself or had taken antibiotics without telling me, wouldn't I have reinfected him? (We were sleeping together 3-5 per week at the time)
You don't say what test was done in June (or April - you give both times). Your doctor is right that no test is perfect, and you could have had a false postive result. But that is more likely with some tests than others.
Your blood test results don't help one way or the other. The chlamydia blood test is not designed for diagnostic testing in cases like yours. The main use is to evaluation of women with infertility, and even there the data are not strong that the results are useful. Your test indeed shows that you probably were infected with Chlamydia trachomatis somewhere along the line, but it could have been any time in your life, such as a distant past sex partner.
In general, the most common explanation for cases like yours is that the male partner has had other partners. Even without treatment, chlamydia generally clears up on its own within a few weeks or months; and people can take antibotics but don't necessarily admit it. So your husband's negative test results don't mean much one way or the other. But there are plenty of exceptions, and you are the only one who can judge your husband's truthfulness. I'm not a relationship expert, but if you have no other evidence he has been unfaithful, it's probably wise to give him the benefit of the doubt.
I hope this helps. Best wishes-- HHH, MD