I would recommend going to your meet, if it's not possible to do both. It's your last chance to compete. (Even if you're running in college, unless you're REALLY good, it's likely to be one of your last opportunities to win or place in a championship meet). Assuming you are going to college, you have four years of parties and frat formals (which are functionally the same as proms but 100x better with more drinking/hooking up and less drama). However, it makes it a tougher choice if you have a date and she is counting on you going. My HS state meet accomplishments and memories are still some of my favorites, even after running in college. I have never once regretted that I didn't go to prom. I'm also a girl, if it matters.
Full disclosure: I was all state several times and state champion once but couldn't have gone to prom anyway because I didn't have a date. haha