In English you can put the 'already' in many places on this sentence and they all mean the same thing.
Are they gone? Why not ''I have aches''..., if they still are remarkable?
Because English works that way. You can't say: "I have aches for two months." Since there is כבר it's a sign that Present Perfect should be used - "I have had aches for two months." That means they started two months ago and they are still here.
Many English speakers would say to a doctor, "I have aches in my back for two months already." You're correct that it's not strictly correct but it's colloquially used quite a bit.
The word "already" should not be used in the sentence in English.