Several ways. Tonsillitis is inflammation (redness, swelling, pain) and/or infection of the tonsils, which can be due to viruses, bacteria, or other germs. Antibiotics to treat tonsil infections sometimes cause rashes. Viruses can cause rashes by themselves or in combination with antibiotic usage. Strep throat causes strep scarlet fever, a well-known rash that feels rough and looks like many tiny reddish dots.
Has to do with. This has to do with the bacteria that causes the tonsillitis stimulating the immune system which causes the rash.