My 1 year old has swollen gums in the same spot on both sides. Does this require medical attention?

Teething? It may be that the same tooth on both sides is ready to erupt. Very often just before a tooth comes into the mouth there can be what weems to be a swelling and a bluish color to the gums over the tooth.
Pedodontist. It's probably erupting baby teeth under the gums in the process of coming in. However, it's time for your child to see a pedodontist (pediatric dentist) anyway for his\her first visit. Schedule an appointment just to be sure.