If you give pain meds at those wakings and she stops waking after, odds are that it's pain of some kind. It doesn't pinpoint whether it's teeth or a latent ear infection, but it's a pointer at least.
Every 3 hours is an improvement, but yeah, definitely not enough for adults to manage the next day, and if she's not getting back to deep sleep after that 3AM waking, she's waking up already OT.....