Shy, introverted, highly sensitive etc are terms that kind of get used but are not the same. Shyness does have to do with social anxiety, and has to do with self consciousness when around people. May even have problems with one on one interactions as well as in groups. According to what I've read, it has nothing to do with energy, rather is more a fear of what others think of you, a lack of confidence.
Introversion has to do with temperament--how they get their energy. Introverts get energized from more inside their heads. They are not necessarily withdrawn or quiet, and can enjoy socializing with friends. Just not too many or too much small talk. If we have to be in a situation with a lot of people, then it is exhausting mentally and we need time, even like a day or more, to recover. Usually don't care what others think of us.
Introverts and extroverts can be shy or highly sensitive, so it's kind of confusing when you're not aware of the differences in all of these characteristics. I think I'm about as introverted as you can get, but still love to get together with close friends for dinner or other events. But if I have to go to something with a lot of people that I don't know well, and sit and listen to chit chat, I don't feel anxious, my head wants to explode from boredom. I'm lucky in that my husband understands 'how I am' and doesn't take offense that I need a lot of quiet/alone time.
You say that your sister says being with someone else is too tiring. That does sound like an introvert. I bet there is a lot going on in her head that you aren't aware of. Having said all of that it's possible that she might also be depressed or is shy on top of being introverted and is NOT happy with her life. My closest friend who was also an introvert, friendly, cheerful, etc. also suffered from depression. You might do a little reading about introversion and then talk to her about it. If she sees that you 'get it' and are not trying to fix her, or cheer her up, she might enjoy talking about how she thinks or feels.
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