The simple answer to your question is that, no, your hair cannot directly cause sinus problems
. A more complex answer is that it could be playing some part in irritating your sinuses because of the dust, pollen, and other allergens (anything that causes or could cause an allergic reaction) that hair can hold. When you shaved your hair, you immediately removed all of that traveling irritation, and it would be quite possible that your sinus symptoms improved very quickly. One of the things that allergist and rhinologists often tell their patients is to change bedding and pillows regularly, and shower before going to bed (including washing hair). This helps to remove everything that has been accumulated over the course of the day, and does play a role in reducing the total allergen load that your body has to deal with every day.
So while your hair itself is not to blame directly for causing chronic allergic symptoms, everything that your hair holds could definitely be to blame. If you decide to grow it back, try washing frequently with a gentle shampoo, especially right before bed. Also, nasal saline rinses are available over the counter, and can be beneficial. Finally, visiting an allergist, an otolaryngologist
, or even your primary care doctor
would offer even more possibilities for overcoming your symptoms of sinus trouble.