My ears feel clogged is it possible to have infection in both ears at the same time?

Certainly: The clogged feeling is unlikely to be infection unless pain is also involved. Allergies or simple URI may cause inflamation and swelling in the eustation tubes, which cause the middle ears to fill with fluid. Alternatively you may have ear wax affecting your hearing.

Yes: At age 35, true ear infections would be rare. Otitis media is very common in kids less than 10yo, & then they seem to grow out of it. More commonly in adults, the ears can feel clogged implying that the ear canals may be filled with wax, which can be cleaned out, either at home or by your fp. Infection would cause exquisite & terrible ear pain; in adults, bright/red/bulging drums need antibiotics.