How can I stop extreme hair fall?

It might be that your underarms have become darker due to some other reason. So, it is best to consult an experienced dermatologist. The dermatologist may examine your condition to know the exact cause of it and determine a suitable treatment accordingly. 

Some hair on the eyebrows falls out each day as part of the natural hair growth cycle, which involves transitions through the growth, resting, and slipping phases. Causes such as anxiety, nutrient deficiencies, uneven hormone levels, or too much plucking might cause hair to fall out excessively. In order to foster the development of healthy hair, consider eating a nutrient-rich diet, drinking water, and not using products that can harm your hair such as perming and coloring. If the hair vasculature starts to thin or you get areas, or the hair loss remains, it is best to see a medical professional. 

You might have a condition called ichthyosis vulgaris, where the skin becomes dry and itchy because it doesn't shed properly. To manage this, it's important to keep your skin moisturized with non-irritating, fragrance-free lotions. Taking warm, not hot, showers with mild soap can also help. Don’t forget to drink plenty of water, as it helps nourish your skin from the inside.

You probably have a red dot that resembles a wart on your private area and is now painful. This might be due to a viral infection known as "genital warts". It is very necessary to not scratch it as this will make the infection spread. Both diagnosis and treatment should be done by a dermatologist. Warts can be removed with medicines or procedures such as freezing or laser therapy.

When certain allergies occur, body parts tend to swell. This might have been caused by contact with something like a plant or chemical that does not agree with you. Ensure the affected area is washed properly. To reduce the swelling, you can use an antihistamine. Seek immediate medical attention if things get worse or if you find it hard to breathe.

From what you are telling me, a cat must have bitten you. And even though it didn't bleed, you saw a burning sensation and a red dot after the event. This is a possible result of bacteria from the cat's mouth. It is important to wash the area with soap and water. Check for any swelling, pain, or redness. If you see anything out of the ordinary, don't hesitate to see a doctor.