Why does this always happen to me?

Whenever I am asked by friends to go out, I always say yes. Whenever I am the one to ask them to go out I get ignored.

Whenever I am asked by my younger sister to bring her somewhere I always agree, but when I ask her to join with me at a cafe, or have a crepe together, or watch a movie together, or study together, she always says no, she’s bored, she doesn’t like it etc.

I feel so lonely and nobody notices that. My mother always supports my sister’s feelings about not wanting to go out. I always end up going at places alone, and that’s more sad than fun. It’s different going out at a cafe to study with company, and doing it lonely. I feel so depressed and have no support. I have the most important examination of my life (up to now) in a month, and instead of thinking of that, I am thinking of why people don’t want to hang out around me...