To create a new person profile in this situation, click that "New Profile" link as you did, then select "Add unrelated people." Otherwise you're creating a profile for a place or a thing instead of a person.
Generally we don't recommend having two profiles for the same person. Obviously, that's counter to our "one world tree" mission. But it might make sense in a few cases and perhaps makes sense for you to do here.
The basic instructions on adoptions are here: http://www.wikitree.com/wiki/Multiple_Parents
Since every person on the tree can only have one mother and one father, we generally recommend choosing whichever you feel is more appropriate and linking to the other parent(s) in the text of the page.
One reason it might make sense to have different profiles for your mother is if her name would be different too. That is, you want to include the name her birth parents gave her instead of the name her adoptive parents gave her. That switches the weight a little more on the side of two profiles.