Feeling very similarly! My advisor at my school and friend who's currently on her Fulbright in Bosnia both said they thought I was an especially strong candidate. Keep in mind (something I'm trying to tell myself) is that they may just be looking for different profiles of people. I know I don't want to be a teacher professionally which may have worked against me. My job search has resulted in only rejections as well, and not knowing what to do after graduation (in a month) is a pretty startling feeling, but lots of people go through it.
If you want to chat more, PM me, because I feel like we're in a similar place! Good vibes good vibes. And anyone who doesn't want their ETA to Malaysia, you know where to find aheather and I
Also congrats to RydraWong! Envious but damn proud.