It sounds as though your T's frustration is probably related to the frequency of your e-mails and/or a general dislike for using e-mails as a therapeutic tool. I don't think establishing a fee for e-mails would solve the problem here. I would recommend asking your T what HER boundaries are around e-mail and then respecting whatever guidelines she lays out.

My T allows e-mail, but only a limited basis. She says it is for those rare instances when a client needs to let her know something or is having an usually difficult time and needs extra support. Since I've only sent her a handful of e-mails over a span of 4 years, she says our use of e-mail has been appropriate and she has always responded. However, she has said that if a client tries to use e-mail too often (i.e. every week), she will establish strict boundaries around e-mail. She says it becomes a problem when the client wants to use it regularly instead of on rare occasions. I told my T to "let me know" if I ever e-mail too much but, so far, she says it has been "the right amount." She has never charged me for the e-mails. Since they are pretty rare, I think she considers them a part of the general therapy package, like the occasional phone call.