Hi Melsie, my friend had the same problem, will your LO take a bottle? My friend had to enlist her husband's help & he just offered her a bottle so they knew how much the baby had taken - when she took a massive 10oz at the start of the night they knew there was no way she was hungry for subsequent wake-ups!! Then they let her cry for just a little bit, as realised they had been rushing to her too quickly without giving her a chance to re-settle.
In my case, my LO never woke quite that frequently so I have just always breastfed her when she cries in the night. I don't envy you as I can imagine of course that's all you want to do in the night when you don't want to wake the house up, but maybe just leave her a little bit to see if she can begin to learn to self-settle? x