What are the little purple spots under and on your tongue?

Normal . With the lack of a clinical exam, i would like to call those spots the terminal end of blood vessels. However if they are new spots that you have never seen before, then you may need to have them checked by a dentist. Some common allergies may be expressed by splotches.
Usually Normal. That's usually normal anatomy. The bottom of the tongue isn't all that pretty, and it can have all kinds of bumps & spots all over. The purple ones are normally small blood vessels near the surface. Sometimes, they can be similar to varicose veins, so they look kinda ugly. You can also get small purple bruises there, from excessive licking or sucking, for instance, your dentist will know for sure.