Is it bad that I really really can't take an interest in doing anything with my youngest sister?

She probably feels sorry for you, and thinks you must be bored, because you're just sitting around doing nothing. She doesn't want to see her big bro brooding all the time. She thinks you don't have any friends of your own to play with, so bless her little heart, your baby sister is going to include you in her happiness. She's only 7, so she doesn't really know what a big grown up boy like you likes to play, so she goes with what she likes best; innocently believing you'll like it too. But, you're still just a mopey old drag, & tell her to go away. Poor lil' girl was just trying to help.

You could talk to her you know. If you work, tell her you want to rest after work, & not play. Same with school. Vome up with believable excuses as to why you can't play with her all the time. If you have friends your age, let her see you play with them, so she knows you aren't lonely. You're old enough to know how to handle this situation. Including how to make sure she has fun with other kids.

You are the one whining here. You are the one acting inappropriately. There are things you can do as an older brother that don't involve dolls or baby games. Such as reading, playing outside (softball, kickball, frisbee, etc). so stop making stupid excuses up for not pitching in with your little sister. Though you are not responsible to entertain her all day, you can do your part and stop being a selfish, self centered brat. If you still live with your parents and don't pay rent, you are 100% obligated to take part in helping out in the household. Get over yourself.

You're 22 you can move out.

You're 22. Move out and then your sister isn't pestering you all the time.