I think your body will adjust but I know it is important to empty both breasts and yes I believe hand expressing is what you would want to do. How much were you pumping before and for how long? New borns stomaches are pretty small so they don't need much to fill up!
You are just starting to establish your supply, you are likely to feel very full until your body and your baby are more in-sync. If you get uncomfortable feel free to hand express a little or jump in a warm shower and let some of the extra run out. Be careful to not pump or express too much as you can easily cause oversupply. If it gets super uncomfortable on a regular basis, deveining cabbage leaves and putting them in your bra can help the inflammation and cut your supply down naturally. I always strongly recommend joining your local La Leche League group and/or getting in contact with a lactation consultant if you need more advice.
Re: Should I feel empty after each feed?