Under my tongue has bluish-purple spots in a random pattern and it is sensitive after eating hot sauce. ?

Varicous veins: We can develop varacosities even in our mouths, especialy under the tongue. If you are having any pain in your mouth, you shoulld consult with your dentist.

Get it checked: Safest bet is to have it looked at by a dentist but the veins under the tongue are large and can sometimes appear as you describe. The skin there is quite thin and may react to the hot sauce without anything being wrong. Hot is often in the eye of the beholder!