Skin conditions are common. They are unfortunately difficult to diagnose without seeing the skin in question. While this may be something minor, I would encourage to see your primary care doctor
or a skin specialist (a dermatologist
To answer your question--YES--people can be allergic to materials in their clothes. This is known as contact dermatitis. Common causes include leather or metals (nickel or gold). Do you wear a chain? Another thing to consider is if there are new detergents that you are using. Fragrances in detergents as well as the cleaning solution itself can cause allergic skin rashes.
Another thing to consider is if the tight collar is rubbing against the skin. This can cause small skin abrasions which result in dry, cracked skin. This is known as xerotic eczema
. It is also common and so wearing bigger collars might help. Your rash may be this.
Sweaty areas are more likely to get an infection. This can be from bacteria, from fungus or even from a virus.
I would encourage you to see a dermatologist. Keeping the area clean, wearing loser collars, and using a hypoallergenic moisturizer may be helpful. If this does not resolve or worsens you may be dealing with a chronic skin disorder. Good Luck.