Is it normal for Invisalign buttons to feel jagged and to really hurt the inside of the mouth? Does it get better?

There are many sizes and shapes to the buttons used with Invisalign cases.  However, the aligners cover them up, so they don't feel sharp when wearing the trays.  The only time you might feel them is during meals, but it shouldn't be significant.

speak to your dentist, they should be able to smooth the sharp edges.  The other thing, the more you put your trays on and off, the smoother those edges will get.  Your dentist knows what he or she is doing, just communicate with him or her! 

As a licensed Invisalign provider, I would suggest going back to your dentist or orthodontist as quickly as possible. Although Invisalign buttons are meant to hold your aligners in place, they should not be jagged, cause discomfort or pain. Your Invisalign provider may be able to swap out the buttons for something that is more manageable and comfortable. Good luck!