How common is it to bleed out after tonsillectomy? how would this be treated in surgery clinic? i read how caroited arteries are very close to tonsils

Depends: Once they cut your tonsils it is expected to bleed but is either cauterized with a special burning tool or pressured, iced until the bleeding stops. It is unlikely that they would damage your carotid artery during this procedure. If you have had a tonsillectomy and are now bleeding please go to the emergency room as soon as possible.

Very RARE: The carotid artery should NOT come into plat with a routine tonsillectomy. Minor post surgical bleeding at the site of the tonsil surgery is common though and your surgeon should be able to control this and tell you how to treat it post operatively. Best wishes.