Should I apologize for acting weird, wait it out, or just let it go? I screwed up!?

Recently, I misinterpreted a friend's actions to mean that he was being completely rude to me and blowing me off, when in reality I jumped the gun and assumed things were definitely planned out, when they weren't.

Like an idiot, I panicked and fired off a letter telling him how I felt about him and pretty much issued an ultimatum: either he would let me know that I was misunderstood in my assumptions or I would take his silence to mean he was no longer interested in being friends. He got the letter and texted me almost immediately to say that he was tired from his travels and he just wanted to rest.

It's been almost two weeks since I've heard from him (that's a little while for us to go without talking), and I feel terrible because I know I was in the wrong BIG TIME for cornering him on something so trivial. I screwed up so badly, and it's keeping me up at night. I feel like I lost my best friend (I know two weeks isn't a very long time, but it feels like an eternity) and I just want him to know I'm sorry for acting crazy.

However, I don't want to come across as being needy and desperate for his attention. I do have my own life, I just don't want to end our years-long friendship because of something stupid.

Should I text/call him to apologize, just wait and see if he comes back around to talking to me (he may have been busy), or should I just let it go and realize that I messed this up?
Updates
+1 y
Oh no, not that long. It may take me some time, though. We've been really good friends for a few years.
Updates
+1 y
I do think he is exercising the part of the letter where I told him that I would take his silence to mean that he doesn't want to be friends. Maybe that's what he wanted all along. I'm simply devastated.
Should I apologize for acting weird, wait it out, or just let it go? I screwed up!?
Post Opinion