Can a sprained ankle break or is it just pain?

No and yes.  A sprain in a stretch and or tear of a ligament, not a bone.  You can twist your ankle and break a bone and you can twist an ankle and sprain it.  Most sprains heal on their own with time and support.  Sometimes, if the ligament tears all the way, surgery is required.

Feel free to seek the opinion of an orthopedic specialist.  They can diagnose your problem and give you a treatment protocol based on a physical exam, x-ray, and or MRI scan. 

You can ice it, rent couches from CVS so you can keep weight off of it, and buy a lace-up ankle brace, but you'd be wise to get a doctor's advice.  

A sprain is a hyperextension (severe over-stretching) of a joint, causing bad muscle fatigue and weakness,  making a broken bone much more likely next time.

Weight off of it until it is no longer painful.   Cheat and it gets bad.

of course it could break, but an exam and maybe an xray is definitive.