How should I resolve a little feud with my older sister?

You share lots of things together and are quite close, she understands you, probably better than you understand yourself, let her see your question on here, show her, how you felt that bad and how you feel that you had to ask for help. She can read your feelings then and know, and she will probably be so pleased that you have shared with her how you feel, because as you say, you probably both feel the same (how funny it would be if she had a question about the same thing on here and she shows you hers lol) anyway, i am sure that she loves to hang out with you and is concerned that you only hang out with her because you don't like to say no, despite your heavy work load, and now after reading it, she will know that she was wrong to feel that way, and you will also know that she loves hanging out with you, so say it as it is, show her your question and have fun, with no more fears about it. It is always best if something is worrying you to meet the situation head on, just ask the question outright, it is far easier to do this and deal with any disappointment if there is any, then to be wondering what if. The quicker you talk to her about this the better for you both. Good luck and take care.