My baby doesn’t seem sick, but if she keeps pulling on her ear, does she have an ear infection?

Not necessarily. Babies / toddlers pull at their ears for many reasons, including ear infections. But unlike the sensory nerves on the outside of our bodies, the pain and sensory nerves on the inside (including the ear) are vague for location. The nerves that go to the ear also go to the teeth, the throat and tonsil area, among other places. The most common cause for ear-pulling is teething. If in doubt, see ped.
Unlikely. Ear pulling by itself is not a reliable indicator of an ear infection. Babies pull on their ears for many reasons, pain in the ear is not usually one of them. They have discovered those interesting appendages sticking out from the sides of their head and like to play with them. Teething can also inspire ear pulling. Just remember, babies usually pull on their ears simply b/c they can.
Unlikely. Most babies with an ear infection appear mildly ill, or have recently been sick. Also, it is common for babies to "play" with their ears. If your baby does not appear sick, they don't have to see the doctor. If they are fussy, or are developing other symptoms, then of course they should be examined.