Hi~ my name is Kim~^^ I am studying English and try to help people who are interested in Korean.
nice to meet you!
It could express either "take care of the old or babies" or pay attention to me or clothes"
In Korean, those two verbs are separated, the first one is "날 돌봐줘" the second one is "나한테 신경 좀 써"
I'm not sure but pronunciation is (날 돌봐줘) nal dolbajuo and (나한테 신경 좀 써) nahante sinkyung jom sseo
However, if you heard it in romantic drama, it will be the second one.