Is there a dedicated public website where I could upload all similar photos and ask people which one is more appealing?
There are quite a few, with Flickr being perhaps the best-known site that's dedicated to photos. Just upload the images in question and see which one garners more "fave" stars. 500px has the same feature, except they use hearts instead of stars. Facebook would also do nicely and has the bonus that you can have more control over the group of reviewers.
So this is not about the "facebook crowd", but "curated circle" of opinions.
Most social networks, Facebook included, let you define groups of friends or associates and share items only with that group. You don't have to broadcast everything to the whole world. In fact, limiting access to the things you share is the feature that's probably most responsible for Facebook's success. The "curated circle" is exactly the point of social networks, and any service designed to provide that is going to look a lot like Flickr, Facebook, or Google+. Heck, Google+ even calls it's groups "circles."
That said, it sounds like you're looking for a circle of experts that's curated by someone else and available for your use. In that situation, you're really talking about something that's more like a service than a social group, and it's hard to imagine why the experts would participate. What's in it for them? Don't they have better things to do than to review strangers' photos? Sites like Photos incentivize that kind of interaction with various forms of gamification (reputation, badges, hats, etc.), but mainly because the "experts" often get to learn from each other.
There are some Stackexchange sites dedicated to reviewing others' work, like Code Review. You could propose a similar site for photo reviews, but it might be tough to get enough backers to make it successful.
I think your best bet is to start with photo sharing/social network sites, but also to work on developing your ability to critique your own work. Reading is one way to do that. Another is taking a photography class where you work on assignments that focus on specific aspects of photography.