When you get a cold or sore throat infection, it is common for fluid to get into the space behind the ear drums and cause pain or a feeling of fullness. This is not necessarily an
ear infection. In fact, there is absolutely no way to tell if you have an ear infection yourself. The only way to diagnose an ear infection is to have your
doctor look inside your ear. Ear infections are very rare in adults; 99% of the time, this is just fluid behind the ear, a normal part of having an upper respiratory tract infection, and this almost never requires antibiotics.
Vertigo, or dizziness, is also a common complication of an viral infection. This can occur either from the fluid collection behind the ear itself, which can stimulate the inner ear and trigger dizziness, or from actual inflammation of the inner ear from the virus. This condition also does not require antibiotics, and it will gradually get better on its own, although often medications to relieve the dizziness are helpful initially.
I suggest that you go see your
primary care doctor, who can perform an examination and figure out if anything needs to be done. I think that the likelihood that you will need antibiotics is very low.