Yes, warm compresses can help release dry eyes. As dry eyes result from the quick tear evaporation due to the insufficient oil secreted by the oil-producing glands in the eyelids, but warm compresses have an effect of loosening up hardened oil that is clogging the glands in the eyelids and keep it flowing better. In this way, warm compresses help the eyelid glands produce more fluid to release dry eyes.
According to your description, I can see that there is something wrong with your eyes. As you can see warm compresses is good for your eyes such as black eyes, sour eyes, and maybe dark circles, however, it has little things to do with dry eyes. I mean, if you want to get rid of your dry eyes, you can try to get some artificial tears and other eye drops to deal with the problem, and try to quit some bad living habits which generate the problem.
Warm compresses can help release dry eyes. The oil-producing glands of the eyelids cannot secrete enough oil to prevent tears from evaporating rapidly, which can result in dry eyes. Warm compresses can loosen up hardened oil that is clogging the glands and keep it flowing better. To be better, you can use a warm compress with lid massage to prevent the softened oil from icky clogged glands.