Oops... sorry. I just realized you said you were bit 3 months ago. Assuming you do have Lyme, you already need more than the standard 3 weeks of Doxy. You'll need to find a good LLMD who will treat you longer if you want to eradicate the infection.
Note: I'm not medically trained, just a long term Lyme patient who has read a lot about Lyme and not fooled by the "standard" policies and treatments for Lyme. I can't diagnose anybody, but if I were you, I'd be running to a LLMD.
P.S. Has your regular doctor run Lyme testing for you yet? Was it at least a month after the tick bite?
... and the strategy of waiting a month to test is unacceptable. Having suffered for years with Lyme, I can't emphasize enough how important it is to treat right away. Ideally, you'd get 4-6 weeks of Doxycycline. About a third of the people who get the standard 3 weeks of Doxycycline end up with long term symptoms of Lyme, suggesting treatment failure. The official dogma that Lyme is always cured with 3 weeks of Doxy is highly controversial with legions of patients claiming they weren't cured.
Pay cash for a LLMD if you have to. It's worth it!
Yes, you could very well have gotten Lyme from that tick bite. The assumption that there will be a bulls eye rash is a bad one. About half of Lyme patients don't get the rash. The official statistics are distorted because a bulls eye rash is part of the reporting criteria. Some doctors mistakenly think they can't diagnose it without the rash. :(
The tick bite and the unexplained knee pain should be sufficient for a diagnosis and treatment. You can easily test false negative for about a month after infection, as antibody levels are insufficient to reach the positive threshhold.
If your doctor won't diagnose or treat you, find another one ASAP. You don't want to get stuck with an intractable infection! Treating it early usually cures it, but you don't want to give it time to get entrenched.