Welcome to the forum.
First reaction, to the title you chose, before reading even the first line of the actual question: The standard HIV diagnostic tests in routine use are virtually 100% accurate by 10 weeks. You did not catch HIV. I'm pretty sure that no matter what I read as I go through your question, you can go forward with no worries that you have HIV and do not need any further tests. What details you tell me about the exposure, your symptoms, or anything else are not likely to make any difference. There simply are no exceptions that test results always overrule such factors.
Now I have read the rest. Guess what?
You describe very low risk exposure (just scan any 10 threads at random about heterosexual exposures to learn why), and your symptoms are not particularly suggestive of HIV (you can also easily find at least 50 threads on this point within the last 1-2 weeks). To your specific questions:
"...how reliable is the HIV antibody test is at 10.2weeks?" Close to 100%. See http://www.medhelp.org/posts/show/1704700
"Is this pain in my neck/throat and chest is something to worry about?" No. HIV wouldn't cause such symptoms; and the test result overrules symptoms anyway.
"What generation are the tests from Kaiser and how reliable they are at 10. 2 weeks?" It doesn't matter. The difference in 2nd, 3rd, and 4th gen tests is in their early reliability, e.g. at 2-6 weeks. At 10 weeks they are equivalent.
"Is there a chance of antibody production after 10 weeks?" No. Perhaps a very small theoretical chance a later test would be positive -- but my 25+ years in the HIV testing business, I have never seen such a case.
I hope these comments have helped settle your fears. You need not worry, and can safely continue (or resume) unprotected sex with any regular partner you may have.
Best wishes-- HHH, MD