Why are my nails peeling and melting?

It seems to be a fungal infection in your left armpit. I suggest you see a dermatologist to look into the rash, and get a medication accordingly. Deodorant should also be avoided as it might make the situation worse.
 

It's so cool that you worry about your family's health. As you have already had chicken pox, you are in all probabilities immune to it. Your dad who is in the process of stroke recovery should not use any preventive medicines on his own without consulting with the doctor. It is a good thing to wash the toilet with Dettol to reduce the possibility of the germs spreading. Pure, practicing the supreme rudiments and caring for one another will be enough to get by!

The signs you are experiencing e.g. Redness, itching, and rashes may be due to various reasons. This could be because of your allergies, stress, weather changes, or some products that could be irritants to your skin. To solve this, you can use gentle skincare products, stop the triggers you might think are causing the issue, and regularly wash and hydrate your skin.

You may have a skin condition known as impetigo. It is usually first seen as a red point and develops into an ulcer thereafter ten days or so, and is finally healed. It may also spread to other skin areas on the body. This is the result of bacteria entering the body through small cuts or sores. In a clean environment, and with the help of antibiotic ointment, the skin can be healed. 

When the itching is only on one side of your body, it might mean that something is irritant your skin. Occasionally, allergies or dermatitis that is caused by eczema can be the reasons for that. Moreover, nerve disorders or infections may be the causes. Look if you have any rashes or skin discoloration. Try to refrain from scratching as it may cause an infection. The application of a light moisturizer or a calm cream can give some relief.

You are very unlikely to get HIV from a barber trimmer. HIV is not spread by inanimate objects like trimmers but through fluids that carry the virus, such as blood. Look for symptoms such as fever or maybe pimples but always keep in mind the probability of this happening is extremely low.

The smoothening change is temporary. Your natural hair will come back in time. Speeding up the growth of your natural hair is possible by using nourishing hair products and avoiding further chemical treatments. Be a little patient, and then your natural hair will come back.

That redness on your nose might be­ leftover swelling. Don't worry though, with some­ gentle TLC, it should fade. Be­ sure to moisturize and use mild products. Staying out of harsh sunlight (and SPF!) will also ke­ep discoloration away. It may take time, but your skin will he­al.