Two things here. I find FB depressing sometimes! But I try to remember that people usually post the best of themselves. Both my sister and my SIL, for example, are constantly posting "did this with the kids, did that, doing such fun creative things". I always felt like wow, I am not doing a good enough job here. Then my sis came to visit and spent the whole time on the couch on her phone, either playing words with friends or on FB! Her kids just wandered around entertaining themselves. And I recently went to SIL's house, where her daughter pulled up her stool at the counter, right in front of the tv to eat dinner by herself. In both cases, this was obviously the norm. That set me free. But it's hard to see what other people post sometimes, I'm totally with you.
The other thing is that you do seem to want to connect with people. So as your son makes friends, invite the other kid(s) over for play dates. Maybe you'll strike up a friendship. As other's said, don't try to piggyback on others' friendships. Form your own. As I've done this, I realized that there are some nice ladies out there. But also that I am not one to be a social butterfly and have tons of friends. I'm more independent and just like to have a couple of friends. You need to figure out what works for you, not just what looks like on FB.
FYI, last year I decided to go a month without checking FB, and honestly it was the best month. I don't go on it much at all now and I'm much happier for it. Good luck to you, good for you for posting, and do what makes YOU happy!