You have conclusively tested negative. An undetected RNA PCR along with negative antibody test at 3 months has ruled out HIV infection. Testing out to 6 months is the most outdated information any one can provide you when it comes to HIV.
It's not uncommon to receive a false positive with IV Generation HIV test since they are highly sensitive and sometimes they pick up cross reacting antibodies, if you have the herpes simplex virus, it might pick that up or it could be just a laboratory error. Whatever the discrepancy is, it has got nothing to worry since you have a conclusive result and it's proven with an undetected RNA PCR that your IV Generation test was a false positive.
Your doctor must have not kept himself / herself updated with HIV testing timelines and protocol. Although it is totally irrelevant at this point, I am curious to know what was your exposure?
No, your result will be the same. I can't imagine any doctor is asking you to waste your time and money. I'd switch to a more competent doctor. False positives happen occasionally and you've confirmed that it was a false positive.