Hello there.
All acts in BDSM comes with a level of risk. It is very important to understand the risk involved l, discuss and decide whether or not to proceed together with your partner. Chemical play particularly involves a lot of risk factors and it is very important to keep in mind that once it's on, it is not something you can safeword out of. Hence proper discussion and understanding of the risks are very important. I'm gonna go on a rant and include things which are beyond the questions. This isn't intended to discourage you, rather to shed some light into the 'not-so-spoken' areas of chemical play.
Any of these items can cause allergic reaction and the person might jot know what they're allergic to. Applying a small amount of the item on the forehand will show whether the person is allergic to it or not.
Using these items inside the vagina, in my opinion, has a high level of risk. I personally would recommend using it only on the exterior parts. But as long as you discuss the risks and accept it, go for it.
Toothpaste has been widely used to create a tingling yet slightly painful sensation on vagina. Please make sure that you don't use excess amount. If it contains menthol, be extra careful as it can turn into a toxicant when used too much or too long. I wouldn't use more than 50 mg of toothpaste at once. Toothpaste being antibacterial can cause bacterial imbalance as well, killing the bacteria which are essential for vaginal health.
Coming to hot sauce, it is an item which is quite often seen among forums as used to create pain and burning sensations. But do realize that it involves quite a lot of risks too. Some hot sauces contain sugar and thereby can cause yeast infection. Be very careful if you plan on using it inside as it can cause damage regardless of how slim the chances are.
Icy hot and vicks are also similiar. Firstly, they're meant for external use only. So getting it inside has a lot of risks. They both have menthol contents. So keep the earlier point in mind. Also the overuse can cause severe damage to the body as it can affect a drastic change in the sugar level which could be fatal. Also, it is not advised to use this if the person takes aspirin.
And here's a few tips if you proceed with it.
*Keep neutralisers like milk, olive oil, benadryl nearby in case the burning gets too much.
*Do not rub. It will only increase the burn. Dab the area with cotton swob or a cloth.
*In case of hot sauce, never put water to wash it off before using neutraliser. It'll only make it worse. First neutralise the effect and then wash it with mild soap.
If you feel this is too hardcore you, you can easily get alternative products in sex stores which are way less harmful.
Have fun. Stay safe.
Devil