my girl decided to leave the internet and her phone for sometime and asked me to not bother myself thinking about what or how she's doing and not to call her sister to check on her

so my question is
should I respect her decision and follow her rules
or to call anyone around her to just check (and that what I want to do )

Well you could do what YOU want and make a perfect pest of yourself, or honor her request out of respect and go about your business. Who dumped who? Sounds like she dumped you. Sounds like this was a distance/social media thing any way and would like to know how long this went on, and if you ever met in person and REALLY dated.

Since she was so detailed in her request: 1) Don't bother to think about what she's doing, 2) Don't bother to think about how she's doing, and 3) Don't call her sister to check on her, I'm thinking she wants you to do exactly those three things. This is called the "white bear" problem, a psychological process whereby deliberate attempts NOT to think certain thoughts make those thoughts more likely to be foremost in your mind. In other words, when you are actively trying not to think of a white bear (or, in your case, your girl), you will be more likely to think about it (her) -- and do all three of those things.

My suggestion is that for two weeks you lie low, get involved with other activities that interest you, and have no contact with her or her sister and don't ask anyone about her. Wait to see if she reappears, wondering what happened to you. My guess is that you won't have to wait the entire two weeks. Then, continue ignoring her. :)

Coming from a mother whose son recently attempted suicide over a similar situation, I say you leave her alone. Do not contact her in any way. Do not contact her sister or any of her friends. Block her number from your phone, block her from all social media. Let her go do her own thing, and you start doing your own thing. In real life, not social media.

I say leave her alone. She does not want to be bothered so don't bother her.
How long have you known this girl and how old are the two of you?