I have never heard someone say that. Haha, I'm young, maybe in a couple more years. Anyways, people usually say 'atleast you are feeling better' 'atleast you are on the road to recovery' 'atleast you are on your way to feeling better.' Hopefully you feel better. Hope you are feeling better. Atleast it is better today. Don't feel bad or frustrated, it is a normal thing to have happen when learning.

No, it isn't unusual and you aren't wrong. To be 'on the mend' is a perfectly normal everyday expression, and it isn't specifically British. If you search this expression online, you will find definitions in American dictionaries and US language sites. I've no idea why your teacher is unfamiliar with this expression. If she is quite young, she may not use it herself, but she should at least be aware of its meaning. Are you absolutely sure that this woman is who she says she is? I'm afraid that it is not uncommon for non-native speakers to claim that they are native speakers, when in fact English is their second language. These people will often use the excuse 'Oh, that's British, and we don't say that in the US' to cover up the gaps in their knowledge of English. Even if she isn't actually lying about being a native speaker, her English may not be perfect. For example, she may have been born in New York and lived there all her life. But if she has grown up in a Latino neighbourhood of the city where Spanish is spoken all the time, she may not have a fully idiomatic command of English. These are just a couple of suggestions. Without knowing more about this person and her circumstances, nobody can give you a more precise answer. But be assured that there was nothing at all wrong with the expression you used. That is exactly what many native English speakers would have said in that situation.

Well, I will preface by saying that I'm a native New Yorker in my thirties and I love old movies, so I have heard the expression "on the mend" before because the character Scottie (James Stewart) uses this expression in Alfred Hitchcock's "Vertigo" from 1958. But I have also used this expression to a slightly younger colleague (late twenties) who is not into film, and she had never heard of the expression either. So I think it might be a somewhat dated expression. However, if you use this expression around a cinephile, we'll understand you perfectly! :D

I live in the southern U.S. and use this expression all the time. I don't believe it is uncommon.

We use that expression frequently in the UK in that context (to express someone is getting better/recovering from illness.) But to let you know, British expressions are less well known in the US than the other way round (i.e. the average British person is more familiar with American expressions than an American is with British terminology.) But I would have thought it was a fairly common expression throughout the English speaking world. But hey, I don't live in the US so I can't really comment further about the frequency of usage there.