If it were the bulb, would my normal lights not work? And why would both bulbs go out at exactly the same time?
Yes your normal headligghts WOULD go out if you hit the high beam switch. There should be either a fuse or a high beam relay under hood or in your fuse box. Try looking up online where to find whichever controls your high beams, whether it be a relay or a fuse issue. Locate it and check it.