To get her to open her mouth, you could try rubbing the side of the mouth. This can prompt some of them to gape so you can get a good look. Check for redness, swelling, bleeding, abscesses, and/or discharge.
I highly doubt it's calcium buildup. It wouldn't happen that quickly, and it would take a LOT of calcium, even if you're oversupplementing, to cause any sort of noticeable physical response.
She's evenly swelled on both sides and across her head. If it was a local infection/abscess or eye irritation, you would expect to see it only on one side, or unevenly on both sides. The symmetry in swelling suggests to me that it could be some type of cranial or oral swelling, possibly due to injury or infection. Either way, it isn't normal, and as XO suggested, an emergency vet would be advisable if you can't get in right away. Best case scenario...this is completely benign and nothing to stress about, and easily reversed. Worst case scenario, it truly is an emergency, and the longer you wait, the worse it will be.