Wanting to get out

I’m a FTM with an almost 3 month old. She’s not the best baby especially at night. Gets really fussy at night. We do not go anywhere but on walks to my brother in laws house, we will go to my mother in laws house and to my moms house. I’m a stay at home mom and would love to make a trip to the grocery store with my LO. I’ve avoided doing this because I’m afraid it’s going to be an awful experience. Any tips or tricks in entertaining my LO? Also do I put the carrier in a big shopping cart? I don’t wanna carry that big thing around in the store!!