Erik,
I agree with Mike's points. I was going to start with his second point. One of the things I found helpful early on was to choose a few genres of photography and focus primarily on those. I continued to do many different types of photography, but I had just a few that I really worked on.
My main genre for several years was macro--both bugs and flowers--and it was early in that time that I stumbled on a very good piece of advice from Scott Kelby. He was writing about flower photography, but the advice applies to many different genres, and your comments about 'snapshots' reminded me. He wrote that one of the secrets to interesting flower photography is finding a point of view that is different from someone just looking at the flower--which is to say, different from a snapshot. The difference may be position, isolation of the subject, some other aspect of composition, lighting, or whatever.
For an illustration, I'll pick a genre at which I am still just a beginner: architectural photography. I recently posted this shot of rooftops in the old port in Bergen:
Most of the pictures I took there were, well, just snapshots when I looked at them more closely. This one I think isn't. I made the roof lines the subject of the photo, rather than the street-level features. I used a slightly long lens (75mm, the longest I had with me) to compress the scene. I more or less followed the 'suggestion of thirds.' Regardless of whether you think it is a good image in the end, it isn't just a snapshot.
My other suggestion is not to rely on friends and family for criticism. Unless yours are much different from mine, most of them will be of no help whatever in this respect. I usually end up explaining to them what is wrong with an image, not the other way around. Find other photographers who can give you criticisms and suggestions. This forum is excellent for that purpose. I also belong to a camera club and make a point of entering images in their competitions because I get excellent criticisms. For example, the next one is going to be judged by a very good night photographer. I am entering two night photographs that I am almost certain will not win because it's an opportunity to have someone who is much better at that genre criticize what I did.
Dan