How old are you? Do you have any other medical condition, such as arthritis?
Perhaps, but viruses are usually self-limiting in a healthy person. I'm more concerned that it may be something more like episcleritis or scleritis. These are inflammatory conditions that affect the deeper parts of the white of the eye. They would not respond to allergy meds or antibiotics. They would have to be treated with steroid medications. If not treated, they can progress to something more serious. These conditions can also be an indication of a deeper underlying condition, such as an autoimmune process. I would recommend that you to see an ophthalmologist. An optometrist would likely end up having to refer you anyways.
Hope this helps.