What can I do for lower eyelid fine lines/wrinkles caused by crying? (Photos)

There are a lot of options to treat this. The main issue is that when you cry you likely irritate the skin in this area and this leads to some swelling.
First thing is first you need to get your depression under control. This is paramount. There are also many options to treat depression these days. From therapy, to exercise and even to medications that are very successful. This will likely make a significant difference in your lines as well and maybe you will not need any surgery at all.
I recommend getting the route cause treated and then if the problem persist you could consider other treatment options. If anything, in some one your age, I would recommend being conservative with something like a light laser or chemical peel. 
Hope this helps.
Best of luck,
DrC

you are way to young to be crying.  please find a professional that can help you.  life is short & you are young.