On Reddit, it's best to find groups for the art type or fan art you want to post about, lurk a little bit because a lot of subreddits won't let you post and participate unless your account is so many months old, then post your best work. If you don't notice traction sometimes it's about the time of day and it's okay to repost stuff. Make sure to have link to another site instagram, tumblr, art station etc what ever you use. it'll help you get followers.
If you want to post on Facebook, I'm not going to tell you not to do it. I just wouldn't recommend it as your sole or main site.Instagram, which is now owned by Facebook, might be a better option. Instagram posts are also easily linked to Facebook pages too.