Good day i have small red, purple dots under my eyes. i am not sure why? i had burning eyes for about 2 days. i also had a headache for 2 days and today there is spots.

Purpura: Those purple dots may well be purpura from blood leakage out of tiny capillaries in the skin under your eyes. The headache and joint stiffness could have been a viral infection or an autoimmune reaction. Avoid aspirin or anti-inflammatory medications like ibuprofen or naproxen and instead use acetaminophen as needed until you're sure that no further spots or signs of bleeding have occurred. See MD