Welcome to our forum and thanks for your question. I'm happy to confirm the reassuring replies you already had on the community forum. It is very unlikely your partner had HIV, which typically is present in less than 1 in 1,000 of even those at highest risk. And oral sex is safe even without a condom, and even if the woman has HIV. To your specific questions:
1) You cannot miss a broken condom; typically it splits wide open and your penis is obviously uncovered. With semen remaining in the condom after sex, you can be sure it remained intact.
2,3) Neither your rash nor pain in your armpit suggest HIV infection or any STD. These symptoms have nothing to do with the sexual exposure a few weeks ago.
4) The oral fluids HIV test is not 100% reliable at 4 weeks -- probably around 80-90%. However, I am positive you do not have HIV; you can expect that any additional tests you have will also be negative. But you need not wait 12 weeks for final testing. If you look for a clinic that does the duo or "4th generation" HIV test, it gives definitive results any time more than 4 weeks after exposure. Or have a standard antibody test (not the oral fluids test) at 6-8 weeks. For detailed discussions of the time to reliable testing, see the threads linked below:
http://www.medhelp.org/posts/show/1891685
http://www.medhelp.org/posts/show/1704700
5) You can safely continue unprotected sex with your wife without worry. (It was never necessary to stop doing so.)
I hope this has helped ease your fears. Best wishes and stay safe--
HHH, MD