Can 9 month old babies have seasonal allergies? And what can they be given?

Don't assume allergy. If I blow pepper in your face, you sneeze ; drain the same as those with allergy. I find babies have more congestion with scented cleaning products, perfume, smoke ; other irritants than they do with animal dander or pollens. The tiny nasal passages that become very noisy with a little mucous or swelling gives many the wrong idea. Nasal wash out with saline nasal spray helps most.
Unusual. Since the child is only 9 months old, it is difficult to make a diagnosis of seasonal allergy. You may try some otc antihistamine/decongestant to see it this helps. If not, contact your pediatrician. By the way, allergic diseases are not usually associated with a fever, .