How to help middle of the night soothings

My daughter is 3 and a half months old and is beginning to cut her first tooth. I know because she's been drooling like crazy and won't keep her finger out of her mouth for anything. Doesn't want pacifier or chilled teether, only her fist or finger (I cover it with muslin swaddle blanket so she can chew on blanket over fist). Naturally, she's been putting up a heck of a tantrum when we try to put her down to sleep. She slept for a while but it's now 3am and time for a feeding and diaper change, but now she's having a hard time falling back asleep. I wonder if soothing her with a story would help, or would it stimulate her mind too much? What has worked for y'all? Advice would be grately appreciated, first time mom* thank you