Can pollen cause such bad allergies that it can make you dizzy and give you headaches?

Sinuses: Allergies can lead to sinuses becoming congested which can cause headaches. That "clogged" sensation can feel like being lightheaded.

Dual effects possibl: Pollen by itself can be an irritant like pepper or smoke & cause irritation to the respiratory tract outside of true allergy. Add allergy & you can end up miserable. In my area we have a common affliction in town when the ceder pollen is flying."cedar fever" can do just that, give some flu like symptoms & difficulty functioning.

Sinusitis: Nasal allergies and congestion can cause sinusitis with postnasal drip and headache. Tender sinuses and ear problem causing dizzy spells and imbalance should be treated with 10 days antibiotic.