This is straightforward contract law. Parties may agree to modify a contract in mutual good faith without additional consideration. If you stated that the contract required modification in fees, because of the changes demanded, then you are entitled to be paid for the change, either in the amount expressly agreed, or in "quantum meruit," which is the reasonable value of services rendered.
The problem is that without a written change memoradum, it's your word against the client's as to what changes would be made and for what fees charged.
If your email was replied to by the client, so that it's obvious that there was a written communication between you, and that the client did not object to your added charge, then that would be sufficient evidence of the agreed upon modification to bind the client. If the client did not reply, then you would have to show that the change memo was received and that the client agreed to that change. This could be an impossible burden to meet, if the client denies having received your email.
That's how it works. You may be absolutely correct and in compliance with the contract, but you will still have to prove in court that the client knew of your additional charge before you continued the design changes, and that the client responded affirmatively to your change memo.
Hope this helps.
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