Installing a door isn't as easy as if sounds. Your mom is renting this house. It's not up to her to decide whether or not you have a door to your bedroom - it's up to the landlord. Your mom may have already asked the landlord about it, and he might not allow your mom to install a door - it MIGHT entail cutting a hole in the wall.
If the landlord DOES allow it, your mom is going to have to go down to building supply and buy a door with the frame attached and have it delivered. That's a few hundred dollars. Then, she's going to have to pay some one to trim out the opening where the door is going to go - they NEVER fit into an existing opening - they always need to be trimmed and fitted. (That's assuming an opening already exists in which a door can be hung). If an opening does not already exist, she's going to have to pay someone to cut a hole in the wall (someone who knows enough about carpentry work to not cut through the wall supports in a load-bearing wall), in which to hang the door, and then install the door and the frame. And don't forget the door knob to go on the door. Door knobs don't come with new doors - they're extra. That's another $25-$30 right there.
You don't know how to install a door, and I doubt that your mom knows how to either. .