Cmpa advice

So when my daughter was born a few weeks after she was prescribed nutramigen for cmpa, when she started weaning the dietician told me if I’m happy to try her with dairy before 1 that’s completely fine which I done and she’s been fine eating dairy! My pharmacy or any near can’t seem to get her milk in so I bought cows milk to try her with (she’s 1 in 3 weeks) she’s been fine drinking it but she’s had abit of an eczema flare up on her hands but she’s quite constipated and did have abit of a runny nose I’m worrying that I’m not doing the right thing and maybe she does need soya or a dairy free alternative to drink. Has anyone had any experiences ect I really don’t know what to do for the best! (Her eczema flares up quite abit on her hands anyways think it’s to do with her putting her hands in her mouth a lot)