Can allergies make it hard to get a deep breath?

Yes: Two reasons - (1) if you cannot breathe through your nose which is common when experiencing allergy symptoms, it can give you a sensation of suffocating (try plugging your nose with your fingers and you will know what i mean) and (2) allergies can trigger asthma which can make it difficult to get a deep breath into your lungs because air can become trapped in the lungs.