Mom Surgery With Blood Clot

My mom, 77, had shoulder replacement 1 month ago. She is currently in SNF and her involved arm began swelling around the elbow and getting red and slightly warm to the touch.

Doppler came in tonight and there is a blood clot. I assume they will prescribe blood thinners and I understand there are "plumbing" techniques. No idea on size since we were with a tech (she could only report findings to the DON).

How serious is this if you can even answer that question with that info?

She is overweight, high blood pressure, kidneys change from partially failing to okay back and forth over the years.

I am the kid who stayed local and am the information hub for my family (which is perfectly fine).

I will of course meet with the doc tomorrow but can't find anything other than treatment on the web.

Thanks for any help if you can work with that info.