Take the baby from the crib and feed her. She will fall asleep quick after she is done. After the burp, lie her down and let her sooth herself. As she is already half asleep, it won't be a big deal. (with full stomach, baby will sleep even longer)
After some days, your breast will produce less milk during the night and you will be able to sleep around 8 hours without being in pain.
I know, my 3 month old sleeps through the night since he turned 1 month. First I was waking up to 3 times to feed him, then 2... Now I dont even have to wake up. Breast are no longer leaking and causing trouble.
Or use the pump.