Sorry to hear of your problem, here's a few ideas . . .
First off if you are able to handle your cow then check inside her mouth/jaw to ensure there is not a lump of impacted cud causing this problem. Sometimes cows when cudding will have a small amount of cud which breaks off and lodges inside the jaw between the gum and cheek skin, this small cud will then become infected and cause an abscess as a result.
Another cause could be penetration by a piece of wire which again will cause an infection, abscess and swelling.
The other option is that it is 'Lumpy Jaw', this is a bacterial infection of the lower jaw-bone, you can usually tell this by feeling the lump, with an abscess it will be [usually] warm and pliable, with lumpy jaw it will feel more solid.
There are other possible causes but without knowing more it's hard to say.
Is your cow losing condition or drooling at the mouth with problems eating ?
You should be fine drinking her milk but remember if you use any antibiotics you will need to take note of any precautions on the label.
Good luck, I hope she recovers.