Is it possible to get a dry socket that wasn't very painful?

Yes but...: Possible? Yes. But in the vast majority of cases, severe pain is associated with a dry socket.

Normally not: Dry sockets are usually very painful. You might also experience a bad taste in mouth, some swelling, smell. I would see the dentist/oral surgeon who extracted the tooth/teeth if in doubt. Do so early on to avoid a quick and really painful flareup.