Baby eczema

My bb suddenly have rashes on her face and body and it’s quite bad. To make matters worse, she is in her drooling stage so it’s really hard. Doc said its probably eczema. I feel so so sad because I feel bad for her and I feel like I failed at taking good care of her. I know she probably has it cos my husband has eczema too but I can’t help but to cry looking at her now. Doctor prescribed her with mild steroid cream. May I know how long will it take for her skin to be smooth again? Any tips on how to manage? Any brands I should use? Im currently using mustela everything. ☹️☹️