Whenever I used to worry about what people might think of me, my mom used to tell me I shouldn't feel that way. But I was shy and awkward, and this was a big concern for me. It was also odd advice, because much of what my mom taught us about how to behave in public was all about what other people thought of us. So her "advice" stunk, quite honestly.
It might be better if you'd try the technique outlined in How to Talk So Kids Will Listen, and Listen So Kids Will Talk, by Faber and Mazlish – listen carefully to her worries and make a positive, empathetic connection. This will help her relax a bit, knowing she has your understanding and emotional support.
Then help her brainstorm possible solutions (skipping school can go on the idea list), writing down every idea either of you thinks up. When you run out of additional ideas, go through the list and discard the ones that aren't effective. For example, staying home a day won't make a difference; she'll still have to go back the day after, and people could have been remarking on her absence. But at least a couple of the ideas could help, and some may bring laughter to the surface (wear a paper bag over her head for the rest of the school year).
This is great training in problem-solving, and kids usually come up with some creative, original ideas of their own. This will also help your daughter come to terms with the role she played in creating the problem.
Good luck. Those can be such emotionally challenging years. Do what you can to help her learn to do her own problem-solving, with your loving support.