The very back of my tongue there are two white lumps. One on each side. They don't hurt, but my tongue does look red. Any ideas what it could be?

Hello ra88

Those large bumps on the top surface of the back of the tongue are probably a type of papilla called circumvallate papillae.. They are located along the "circumvallate line" and contain taste buds that confer the sense of sour and bitter to the back of the tongue. They can actually be quite prominent and are often mistaken by patients for cancerous growths .

Look at Figs. 1.37 and 1.39 in this article called Examination Technique with Normal Findings and Structures Mistaken for Disease for pictures of normal appearances.

Please ask your dentist or doctor and let us know.

Best wishes
Vinod