They are grammatically corret but there can be a slight difference between "take after" and "look like", the former meaning not only do I look like her but my character might be similar too.
a. I look a lot like my Mum/I look very much like my Mum/I really look like my Mum.
b. I take after my Mum a lot (I think it's OK but it sounds a little strange)/I really take after my Mum.
I second your opinion,it could mean that you have inherited some character traits from your mother besides the physical similarities.They are grammatically corret but there can be a slight difference between "take after" and "look like", the former meaning not only do I look like her but my character might be similar too.