Cat people

So I got a new cat and I have 2 other pets. I’ve had her in my room for 4 days and she doesn’t wanna leave my room cuz she’s very comfortable in here

My mom thinks I’m keeping the cat held captive in my room and not “allowing” her to leave my room. I let the cat out of my room and she made it to the living room and ran back to my room cuz she got scared. My mom then said I was immature for keeping the cat to myself and not letting her out.

The cat has her litter box, food and water in my room so that’s not a issue. My mom thinks I’m not doing a good job at this whole cat thing. Also my cat is 3 years old. Is she in the wrong or am I in the wrong?