It is unlikely that she is truly emptying your breasts, although it definitely feels like that sometimes!
Cluster feeding is totally normal at this age, and 3 hours sounds normal too. I understand why you are offering formula (been there, done that), but in my experience, just relaxing and feeding more actually satisfies the baby more, as it gets your supply to regulate. The more you feed, the more milk your body makes, it's pretty cool actually! Plus which, all the washing and sterilising bottles and preparing formula actually negated any rest I got by giving DS a bottle of formula when he was wee. Are you switching between boobs when she seems dissatisfied? That always worked for me. And keep yourself hydrated and fed, so you feel OK too.
Do you have a local LA leche league you can talk to, as they are generally great for support at any stage of breast feeding, and can help you decide the best approach for feeding your baby.
But for now, just going with the flow should be enough - for the first few weeks, baby wants to be close to mum all the time anyway, and normally feeding all the time too, to get your supply up. Enjoy the cuddles while you can :)