It is hard to determine what could cause the types of symptoms you are describing.
SwollenSwollen glands neck glands are common following drainage from allergy symptoms and infections of the throat and sinuses. These swollen glands do not usually cause pain in the back of the neck. Because the pain in the neck gets better with a hot shower, this may indicate some tension, which is causing the pain that is relieved by heat. The pressure and pain behind your eyes may or may not be related to the sinuses. With all that you are experiencing, it may be reasonable to talk about having a CT scan of the sinuses with your doctor. This would show if the sinuses are inflamed or infected. If this is the case, it could have a lot to do with what you are describing.