Can a pet allergy cause your nose to plug, give you a sore throat and a bad cough?

I recently adopted a puppy. I felt fine for about a week an a half, but 2 days ago I began to sneeze alot. My nose plugged and I had to blow almost constantly. I also came down with a sore throat and a bad cough. Is this a result of a pet allergy or did I just come down with a cold? I've been around dogs all my life and I don't ever recall reacting like this before.

 It really depends on what breed of dog you have and if they have hair or if they have fur. Certain breeds have hair which needs to be trimmed. These breeds would be a cocker spaniel or a poodle and they don't shed like fur. This is one reason people who have allergies tend to get these breeds. They are often called hypoallergenic breeds though really there is no such thing as a completely hypoallergenic breed.