I've been in your position, so I understand how you feel. Here's the thing: You have excellent family photos, well above average for Facebook and family photo albums. And for many people, they feel that once they get better than their Facebook friends, that puts them in the realm of professionals. However, that's not the case. There is a huge gap between the best family snapshots and the lowest tier of professional photographers.
Right now, your biggest focus should be building a portfolio. Ask friends and family if you can do portraits of them, ask for critique on the photos, then take more. If they turn out well, great! You have pictures for a future website, and the family has photos that they'll put in their home or on Facebook. Then when you're ready for business, all of your friends and friends of friends will be somewhat familiar with you as a photographer, and you'll have your first set of clients. After that, you'll have to work harder to expand from that small circle, but that's a discussion for another time.
In my opinion, a good portfolio should have about 15-20 photos from about 10 photoshoots, and feature a fairly diverse set of people. Different ages, different ethnicities, different body types, etc. It's fine if you want to specialize somewhat...for instance, if you want to primarily photograph children, there's no need to have boudoir shots in your portfolio. But you should have babies, toddlers, and school age children. After you have a name for yourself, you can choose to specialize even further (I.e. only newborns, only high school seniors, etc.)
Anyway, just my thoughts on the topic. You have talent, don't give up. It's just going to take a little more work to get you to where you need to be.