Interestingly, there are two major forms of allergies - eye allergies and nose allergies, called allergic conjunctivitis and allergic rhinitis, respectively. Although many people who suffer from allergies do have both allergic conjunctivitis and allergic rhinitis together, it is entirely possible to only have one or the other! Therefore it is possible to have itching, redness, and tearing of the eyes, representing allergic rhinitis, without accompanying sneezing and nasal congestion.
I would recommend that you go to see your doctor
. They will be able to confirm a diagnosis of allergic conjunctivitis. Fortunately, there are excellent medications that can be used to treat allergic conjunctivitis, including non sedating antihistamines like loratidine (claritin) or cetirizine (Zyrtec), as well as various eye drops that your doctor can prescribe for you.
It will also be important to think about potential sources of the eye allergies. Common offenders are "indoor allergens" like cat or dog dandruff, mites, mold, and fungus. If you can identify the offending agent, it makes it easier to deal with the symptoms, as you can work at removing the allergen (for example if the problem is mites, you can put mite covers on your bed mattress).
Start by talking with your primary care doctor