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It appears that you are experiencing dizziness associated with vertigo and double/blurred vision, which is seasonal. While your symptoms may be in part be related to seasonal allergy as a trigger, but it is likely there is an underlying susceptibility of your sinuses that make it easier for you experience this persisting seasonal problem. At the back of the nose, inside, there is a common meeting point between the nasal, ear and eye sinuses. With chronic or recurrent inflammation of these sinuses, any exacerabtion by seasonal allergy can cause imbalance of the fluid/pressure within and outside the sinuses, and so can cause vertigo and dizziness (ear sinus related) blurred/double vision (due to nystgamus-due to effect/pressure on the orbital sinuses).
Although you need to continue with your current medications focused on reducing your allergy and inflammation, I suggest that your doctor closely evaluate you with CT Scan and/or MRI of the sinuses to exclude any persisting chronic infection that needs to be treated with a more effective antibiotics. Augmentin, instead of amoxicillin, for a longer duration may be necessary.
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This is for information only, and should not replace the recommendation of your doctor.