A lot of the things mentioned, Ben Gay, Vicks, Mentholatum, Tiger Balm, Icy Hot, and the such, are meant to increase and stimulate blood flow to the applied area. Not having any of these laying around, I'm sure if the labels are read, they would probably specify 'for external use only'.
Granted, we all experiment, we all have our kinks, and will do things out of the ordinary, however when to increase or stimulate that blood flow internally, especially into the rectum, there is a good chance of aggravating
any existing hemorrhoids, or maybe even possibly causing hemorrhoids.
Hemorrhoids are just veins inside the rectum that we all have, that become swollen or inflamed. And using such products can certainly 'inflame' that area, and over a period of time, I personally suspect can result in full blown hemorrhoids that bleed.
Certainly with any kind of anal play, during/after enemas, or just the internal application of these products for that extra stimulation, remember that there's already a rush of extra blood running through those veins. So I would tend to guess with any kind of aggressive anal play or 'pushing limits', can certainly result in some internal bleeding.
I've suffered from bleeding internal hemorrhoids for many years, and after many years of treatments now, I am pretty much 'fixed' of them. Over those years my activities were really limited, (and very frustrating).
Now that I can say I'm fixed of them, I certainly wouldn't want to do anything that's going to bring them back! So nothing stronger that a little mild soap for me... I'm sure that applying any of these products to say a dildo or a butt plug would result in a 'rush' of intensity, (that I'm sure I would even enjoy), but at what possible risks?
There's a lot of other ways to add some stimulation in ones play, without taking such risks.