Milk allergy

I’m a FTM and exclusively pumping Today we went to do monthly check up on my baby girl she’s 1 month and 2 weeks old She weigh 4.50 kg and doctor recommended to give her formula for 2 main reasons In his opinion she under weight and the second because of milk allergies i showed him a picture of her diaper and there were mucus in it and he told me its a milk allergy.. even tho she’s a good baby sleeps well, feed good not colicky but we do have these minor gassy night and we do bicycle exercises and it works well for her .. also to mention im eating Greek yogurt 3 times a day since i give birth.. its just an easy quick snack so maybe thats why she have the milk allergy , and is this condition serious? Im stressed to give her formula but at the same time i want whats best for her