I had the flu and was puking all night, now ihave popped blood vessels on my skin and my head hurts everytime I cough, will this pain go away?

Yes. If this is in fact influenza you will get better over a period of two weeks or so. Unless you get a secondary bacterial infection you will not benefit from an antibiotic. As long as you are not getting worse after the miserable first five days or so you will continue to gradually improve. If this is influenza it helps to understand why flu shots are recommended.