Your cheeks are being bitten due to which you're suffering from traumatic stomatitis. It sounds fancy but is just a simple cheek bite.
As for your lower teeth swelling, I am assuming it is a mandibular torus (bony outgrowth) but an xray is crucial to confirm the diagnosis. Either way, it is nothing to worry about.
Next Steps
Your cheek bite can be treated with a topical ointment which is antibacterial and anaesthetic.
Health Tips
Enameloplasty (grinding of the concerned teeth cusps which are sharp) will help you from not having cheek bites again in the future. Good luck!