Yes you can put some hand sanitizer under your armpits and the hand sanitizer will help kill bacteria and keep your armpits from smelling bad.
Just be aware that some people have allergic skin allergy reactions to certain stuff including hand sanitizer and it might cause an allergic reaction under your armpits but I put hand sanitizer under my armpits and nothing bad has happened.
I don't do it often but when I sweat more I use hand sanitizer to kill the bacteria that causes armpit smells.
Too much use of hand sanitizer can burn your skin and it can also lead to drying out your skin and cracking it and potentially lead to bleeding as well.
Some people are also allergic to the hand sanitizer which can lead rashes and skin burns due to the skin allergies from the hand sanitizer.
Most times though when hand sanitizer is used in moderation it causes no skin burns or rashes.
Yes it is bad to use hand sanitizer too much because when you use hand sanitizer which is alcohol based too much then you can cause your hands and skin to dry out which can then lead to the skin on your hands cracking and possibly bleeding.
Hand sanitizer should be used in moderation to keep your hands germ free especially during cold and flu season.
But you should also wash your hands with regular soap and hot water to keep your hands clean and flush the germs away down the drain.
You also need to wash the hand sanitizer off your hands before touching food because you'll get the taste of hand sanitizer in your food and it doesn't taste good.
When you use hand sanitizer to sanitize your hands you should wash your hands with regular soap and water to get rid of the hand sanitizer off your hands.
When you touch food after using hand sanitizer the hand sanitizer will transfer from you hands to your food which is not good.
I once made that mistake and after cleaning my hands with just hand sanitizer I grabbed a sandwich and started eating it.
I got that awful taste of the hand sanitizer in my mouth which I had to then wash out of my mouth by using mouthwash a few times.
So while hand sanitizer is good for killing germs on your hands it's required that you still wash your hands off using hot water and soap to keep from transferring the hand sanitizer to food.
Or put on food grade gloves when you've used hand sanitizer on your hands before touching food.