Such a rich network of veins are present in the scalp and temporal areas of the face that this scenario that you are describing does not occur. There is localized tissue swelling and even this is unlikely as the head is above the level of the heart and by gravity, venous drainage is aided and venous pooling in the area is minimized. We recommend the use of a bioflavonoid formula after cosmetic and vein procedures which minimizes tissue swelling - called Swell-X and available from an online store.
Temporal veins can be treated in multiple ways. Following treatment there could be swelling over the temporal area or over the eye due to local irritation from the treatment itself. This swelling is due to local tissue trauma not due to back of blood from blocking or removing the vein. If swelling should occur, it it usually treated with ice packs and it should resolve over about one week. There should be no permanent swelling of the face, eye or temporal areas after the treatment.
The most important thing to consider when thinking about treating blood vessels in this area is to be sure what you are trying to treat is a vein and not an artery. Veins are most often blue in appearance, very soft, and have no pulsation in them. These vessels are very readily treated by either removing them or injecting them. After having them removed there is likely to be some temporary swelling related to the procedure but there should not be any long term concerns with swelling. The artery in this neighborhood is called the Temporal Artery and is often bulgy in thin people. This artery has a pulse in it and you can often see it pulsating if you look at it closely. The Temporal artery should really never be treated for cosmetic reasons.