I've been having pain in my mastoid process and I haven't done anything to it. It feels swollen compared to my other side. Any advice?

Possibilities. It could be a muscle strain, inflammation of the attachment to the mastoid process, or a tear in the same area. I might suggest seeing a specialist in craniofacial pain for a diagnosis and appropriate treatment. You can go to www.Aacfp.Org for a list of dentists.
Tmj. You likely have tmj. A way to tell is to open and close the jaw with a finger placed in the TMJ socket which is roughly the pocket created when one opens the mouth and places a finger directly in front of the ear canal right at the level of the sideburns. Softer foods, warm compresses and Motrin should help. Avoid gum chewing. Other option is migraine. A swollen mastoid is rare see ENT or get ct.