I don't feel she's being hypocritical at all. It's completely understandable because of who you're helping. Sage is, for all intents and purposes, just some girl. She isn't your sister or mother or something, she's a potential rival for your affections and technically "just a friend" at that point. Sure, she's sick, but she isn't dying, and she could very easily either take care of herself, or have some other person take care of her instead of the MC. Sage wants the MC to come help her because she likes him. Jill realizes this and is hurt you pick Sage over her, especially with a date to a special place planned out.
At least that's how I see it.
(and for the record, I don't really have a favorite between the 2 of them)
Jill will bite herself in the ass because she is well on her way to becoming friends with Sage. She will learn so the MC helped Sage when she was sick in bed.
Are you still thinking what Maya said to the MC in EP3 when she asked him what he would do if he was rich all of a sudden. The MC said so he would renovate the house for and with his father and it would make him happy to see his father happy about it. Maya answered that this would be very unselfish of the MC.
This unselfish can be applied throughout the game. Just help Sage with her problem with Chad and then when she wants to kiss the MC, turn it down. Turn her down when she's playing guitar, etc.. All unselfish help.
With Jill it's a little different. Jill helps the MC whether he wants it or not and the MC makes up for his debt to Jill. The same thing Jill and Isabella will do for the MC, because without ulterior motives he helps Jill to fulfill her biggest wish. The concert. This touches Isabella and Jill deeply and they will not forget it. Jill even says so she will never forget this evening.
This is also the reason why Jill wears the banana or bee costume. When the MC is on Jill Branch and the princess successfully saves Jill from Tybalt, Jill doesn't get the confidence she would need and goes into a sentimental dependency on the MC. But if the player is not on Jill's Branch, helped her at the concert and does not save her from Tybalt, she will understand so that the MC only gave her the push to overcome her stage fright. The rest of the concert she played alone on stage. She can build on this accumulated self-confidence. The MC also proves so that he helped her without having ulterior motives regarding sex.
Isabella is overjoyed because the MC has accomplished something that she could not. She herself has been trying to get Jill to stop being so naive by talking to her. But she did not get through to Jill with the talks. The MC, on the other hand, didn't talk to Jill about it, but he taught Jill through the concert.
The whole thing culminates in EP9 when Jill, Maya and Sage talk. Sage already knows that the MC helps unselfishly. That's why she helps Maya. But she has the wrong idea about Jill. Why? Tybalt doesn't do anything unselfishly and Sage thought all along so Jill is just like Tybalt. Sage is proven wrong and the two become friends, I'm sure.