I am wondering if there is a way to directly communicate with users from the photography stack exchange site or any of the stack exchange site where we are not using comments to communicate with each other?
As noted in the Meta.SE question JNat linked to, and in the related Meta.SE question, How do I contact other users?, the only out-of-band / user-to-user contact facilitated by Stack Exchange is if a user explicitly adds contact information to their profile (i.e., personal website where they might provide a contact link, Twitter handle, Github account name, etc).
In essence, Stack Exchange's outside contact policy is strictly opt-in for users to allow themselves to be contacted, and entirely under that user's control to determine the means of contact, by publicizing whatever information about themselves they wish.
In general, this is bad. I understand your desire to be helpful, but it's an approach that doesn't scale. We want open (and openly-licensed) content that has a long lifetime, making the Internet a better place. One-off help requests don't do that.
And, again while I understand the urge to be helpful in individual cases where someone has a classified-ad style request, I'd like to encourage everyone to hold back, because there are an infinite number of such requests out there, and one attracts another, and the net result is a lot of noise — bringing down the relative amount of signal, and making the site less helpful to the general public overall.
Aside from being contrary to the goals of openness and creating long-lasting content that helps many people, a direct communication channel would also be ripe for abuse. Answering and commenting and chatting in public forces users to mind their manners or suffer the consequences of public disapproval and swift moderation. A private communication channel would be a vehicle for harassment and abuse. The moderators have their hands full as it is -- they certainly don't have time (or desire, I'm sure) to sort out complaints about direct messages between individual users.