(((Soup Dragon)))
We've bumped into each other in a few other threads, so you know, I find therapy extremely ridiculously hard too, and am about ready to quit as well. (Ha - and since misery loves company, I kind of want to run around telling everyone else to quit - I have to watch that, maybe it's projection?

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Am I understanding correctly - you emailed your T a simple request to change your appointment, and she didn't respond, and that's what's making you feel bad?
I feel really awful too when my T doesn't respond to emails. To the point that I just do not email him, unless it's something like administrative, like schedule changes. There's just no point in putting myself through that!
But in this case, I can't understand why she wouldn't respond? There was nothing else in your email, right? This is administrative, and she *should* respond so that you guys can get your schedules straightened out. There's not really a good (therapeutic) reason for her not to respond (it's not something you really need to "sit with your feelings" about!

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So, that makes me wonder, like others have mentioned, if something could have happened. Sometimes emails don't make it through to the recipient (weird, I know, but true!). Sometimes people see them but can't respond right away, and then they get buried by other emails. Sometimes people have emergencies, or their computers break, or something else happens so that they can't get to their emails.
How long has it been since you sent it? Is it urgent (i.e. rescheduling your next appointment, versus one in a couple weeks)?
If it's urgent, and it's been more than a few days, could you resend it? What I do is... go to my "Sent" folder, forward the message that I sent to the person, then add a note at the top saying something like, "I'm not sure if this made it through and I haven't received a response from you, so I'm resending. Is it possible to reschedule next week's meeting? My boss is sending me to Timbuktu, and I won't be in the country on Thursday. Thanks!"
Good luck, and try to hang in there... this seems like a very "fixable" thing. Not to say it doesn't hurt, I think anytime it feels like someone we like/need/count on/care about doesn't respond - it feels like we're being ignored and *hurts*.
But hopefully it was an honest mistake on the part of your T!