First, it sounds like you have no actual idea what those people were talking about, you just assumed they were talking about you. Maybe they were, maybe they weren't. You didn't hear them. Have you ever asked anyone you actually know if you smell or not? Like someone in your family or a friend? Do you smell yourself? Because it sounds like you're assuming all of this stuff to the point you've given yourself a worsening anxiety problem. Whatever is going on, if you let it fester it will get worse, so I highly recommend you find a psychologist and begin therapy as soon as you can to treat your anxiety. I wouldn't recommend retreating to your home -- it will make it worse.
Paxiled always has great advice. It seems like you know anxiety is an issue and seems to exacerbate your symptoms. Getting into counseling to treat your anxiety is a great starting point. However, you may want to talk to your primary care provider to rule out underlying medical concerns. You can also have them check out the rash under your arms. Prescription deodorants are available. You might also want to try hydrocortisone cream on the rash. As tempted as you might be to stay home and avoid contact with others, it will just feed the vicious cycle of anxiety. I wish you all the best.