Well hey, if she wanted to have dinner with you that night (on such short notice, it was the same day you e-mailed her right?) there's a large possibility if you tell her the truth she won't object at all to having it tomorrow or perhaps another time. Put yourself in her shoes, she's not going to be offended by you simply not checking your email soon enough. Relax and keep postive about the situation, I'm sure it's fine.
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Ignorance is surely not bliss, because if you are ignorant, you will ignore the bliss around you.