I am a man who was having vaginal sex with a woman. I wore a condom. After sex, I pulled out and it appeared that the the condom was intact (ejaculate at tip of condom). However, I felt lubricant on my penis (which I think shouldn't happen if it's worn properly) and my partner says she felt something sudden and warm at some point. 

Is it possible the condom broke/I wore it inside out and should I be worried about STI infection? 

Welcome to our forum. Thank you for your questions. I’ll be glad to comment. When condoms break, they break wide open, leaving no doubt that they have failed. They do not leak just a little or reseal after breaking. The lubricant on condoms typically is present in the package and on both sides of the condom. I cannot state this to what you and your partner felt but from the sounds of things I would be confident that the condom did its job. EWH. ---

To shift gears a bit, I had sex with condoms 9 days ago and five days ago with separate female partners. About three days ago I started feeling sick with sore throat, no fever, joint weakness, night sweats. I assume the risk of HIV is so low that I do not need to get tested. I probably will anyways just to be safe but wanted to confirm risk is low.

As long as condoms are worn throughout an exposure, there is virtually no risk of HIV.  In studies of persons seeking care for flu-like illnesses, over 99% have something other than HIV.  EWH---

Final question:

What is the probability that a person who contracted HIV (I know odds of this are super low) would have a negative RNA PCR test at 11 days after the encounter? At 6 days after exposure?

I really appreciate the service. Thanks.

HIV RNA PCR results at 11 days are considered conclusive.  EWH---