Sorry to hear you are having these symptoms! If you have not seen your primary care doctor
about this issue, I would recommend that you do so. It is very common for people who have had a history of seasonal eye allergies (allergic conjunctivitis) to also develop seasonal nasal allergies (allergic rhinitis). If you have allergic rhinitis (or resulting chronic sinus congestion), this can definitely lead to sneezing, congestion, and chronic cough due to mucus dripping down the back of the throat. Your doctor will be able to examine your nose and throat and help determine if this is going on in your case.
If your doctor does diagnose you with nasal allergies or sinus congestion, there are several different medications that can be used effectively to relieve these symptoms. In addition to the standard anti histamine medications, which you may have already used in the past for some of your eye allergy symptoms, there are also inhaled nasal steroid sprays which are particularly effective at reducing nasal symptoms. Irrigation of the nose with a saline saline can also help to clear out congestion and mucus.
Start by seeing your doctor at your earliest convenience, and you should be feeling better soon!