Baby allergies?

Hello, I recently moved from wyoming to Nevada & my 5 month old has had a very bad runny nose for the last two days now, I am using the bulb n saline drops, I was curious if babies could have allergies & what helps them? First time mom! Still learning new things, he has no fever though! Small cough every now & than so I’m confused if it’s a cold or something different like allergies I still am trying to find him a doctor I love 70 miles from any place with a hospital and the clinic in town has a list full of people before us