Hi, OP —
Academic here. I am sorry about your illness. Your situation is tough.
First, I wonder what country you are in? Your mention of A’s and the specific reminder by the lecturer that ‘this is an Honours course’ don’t quite sound British. Expectations and cultural norms may vary a bit. I’ve taught in American and British universities so I will stick to generalities, and those systems.
Gently, I agree with PPs about the asynchronicity of email. I rather wish we had such a regulation! It is to disabuse (mostly young) students of the notion that they have a right to a quick reply when emailing us in the evening or worse. But we could not function without encroaching on our personal time to respond to student emails.
Of course all student queries should be treated with respect. It is wrong that yours wasn’t. If you separate out the (really nonexistent) email issue, is it still as bad? I am guessing ‘yes’. Is the trouble restricted to this communication or is there history? Is this lecturer aware of your health issue?
Regardless, I don’t see anything here that rises to the level of an appeal. Appeals are for disputes over formal decisions. However in your shoes I would show this message to someone I trusted at the Office for Students with Disabilities (whatever it is called) for advice. Of course the Student Union is also an option, possibly a very good one - IMO SUs are a bit variable.
A complaint is a different matter from an appeal. You’re entitled to make one. The question is whether, like many issues in the business world, this is best resolved informally. If there is no history your msg may have caught the lecturer at a bad time. Or, there is a possibility that the tone was different from what you intended. Everyone has surely sent a few such emails unintentionally. This is why I think showing both messages to someone for feedback is your best bet. Good luck