A Doctor Removed a Bulging Vein in the Middle of my Forehead?

Thank you for your question. Some areas around the face are not safe to treat due to risk of blindness. I would recommend consulting with an opthamologist or vascular surgeon for safest and best treatment option. I hope this helps.

These are superficial and cosmetic veins and treating them will have no untoward consequences and will NOT cause problems with arteries as you have suggested. 

What you had done is an accepted form of treatment for these types of veins.   Initially you may have some swelling and even bruising but over a week or so it should resolve and I would expect you to have a very nice result. There should be no long term effects to any other facial or body veins and there is no relationship to your temporal artery.  Be patient and allow time to heal.

The mid forehead vein drains the scalp and forehead. There should be no harm to the arterial supply. Other veins in the scalp and forehead will take over the blood drainage and no harm done because these are superficial veins.