Stubborn dandruff may be caused by a fungus on your scalp that causes the skin cells to accumulate and become flaky. Scratching too much could also be the cause of a sore head. Use a medicated shampoo that treats the fungus and calms your scalp; additionally, wash your hair gently and frequently.

Psoriasis can be a bit challenging to treat but various treatments like medications, laser treatments, alternative treatments like homeopathy etc., avoiding triggers that worsen your psoriasis symptoms can prove useful. I suggest talking to your doctor for proper examination of your condition which will help in deciding which is the best treatment for your condition. 

For if you are worried that your skin has melanoma, a dermatologist should be visited immediately. Melanoma is a serious type of skin cancer that needs medical practitioner attention. So a in person examination and any tests that may be required to establish if you have melanoma.

DANDRUFF NEEDS daily care.. Use MEDICATED SHAMPOO.. Avoid hair styling products... Try TEA TREE OIL.. Reduce STRESS.. See a dermatologist if severe...

Looks like your daughter has a skin irritation that is contact dermatitis. One common type is contact dermatitis, which is caused by something rubbing against the skin and triggering redness, itching, and swelling. This thing might be her bra strap or shirt, which is the cause of the rash on her skin when it rubs against it while she is playing basketball, To make her feel better, try to use a soothing lotion or cream and let her put on clothes that are not tight enough to prevent rubbing as much as possible.

Your scalp problem could be a medical issue that requires medical treatment. I recommend you should pay a visit to a dermatologist, who is a skin expert. They can detect the condition and recommend the medications or treatment option that should be taken. Avoid using any harsh chemicals on your scalp until you have been to a doctor.