Capsaicin is derived from pepper--it's what makes it burn. Eating capsaicin actually helps to prevent clotting, but as a topical, it shouldn't have an effect either way.
I found a mainstream medicine link for you to read more. Note that when it talks about antioxidant action, it's not referring to topical application:
http://www.webmd.com/pain-management...topic-overview
I do not use muscle rubs (because I think they're dangerous), but capsaicin isn't anything like salicylates. I would caution you, however (and I should have said something in my first post), that you should test a small area of the skin first to make sure you're not sensitive. No matter what, you will feel burning the first couple of times you use it, but if it is extreme or if it persists, then capsaicin may not be for you. Happened to a friend of mine after he let me put it all over his back. Not pretty.
As for your thyroid, use caution reading your lab results, and make sure they test FT4 and T3 or FT3, not just TSH. Also make sure that when you test, it is at the same time of day and under the same conditions as your last test.
When I had mine done recently at CINJ, my FT4 was very slightly higher than normal, but that's because the test was done at midday after I'd already taken my medicine. (I take 200 ug Tirosint/day because autoimmune thyroiditis left me with a non-functioning thyroid.) Normally, I have labs done early in the AM, before both food and thyroid hormone, so there was no doubt I would get an inaccurate result. I just let it go, though, because I have an order from the endo for later in the month, and those labs will be done correctly.
I don't like the smell of vinegar either, but I've learned to get used to it because it is so useful, both in the body and around the house. Okay, maybe it's not that I've gotten used to it so much as I've learned to breathe around it. Also, I sit outside on the porch when I soak my feet. Now that it's cool, I'm pretty bundled up, but it's better than the alternative.