I said “ my arm aches me “ and My teacher said “the arm sores not aches “ So both of the words describe illness , what is the wrong with using arm ache ?
Some note needs to be made of the difference between "ache" and "pain", from a sensory point of view.
ache typically refers to a discomfort felt over a relatively large section of the body. Eg, you might say that your shoulder aches or your thigh aches. The discomfort does not have any strong focal point.
(Of course, English being what it is, a headache breaks the above "rule" and often has specific focal points one can identify, vs being felt generally over a large part of the head.)
pain is more general, and, in some contexts, an ache is a type of pain. But usually "pain" implies a discomfort that has a focus -- a particular point in the body that hurts, or perhaps (in the case of a muscle strain, eg), a distinct line of discomfort that is felt in the body.
sore is another word that has different implications in different contexts. When you exercise hard and complain that your muscles are sore the next day, you usually mean that they ache -- there is typically no strong focal point for the discomfort. But if there's a particular point on the body which, when pressed, produces significant discomfort, that's typically referred to as a "sore spot" or something of that ilk.
A pain, of course, is trying to keep all this stuff straight if you're not comfortable with the language.
Ache, denoting a dull, continuous pain, is intransitive, so while you can say
My arm aches.
You cannot say
*My arm aches me.
Sore, however, is not even a verb, but an adjective (or noun), so you can say
My arm is sore.
*My arm sores me.
Pain can be transitive, but today is almost always used figuratively:
It pains me to have to accuse one of my dearest friends of being a hypocrite …
"My arm aches" is proper. I believe that "my arm aches ME" is incorrect because "aches," used as a verb, does not take an object like "me." Saying "me" is redundant, because only you can feel your arm ache.
"The arm sores not aches" doesn't make any sense. You could say, "My arm is sore." "Sore" is not a verb and so "my arm sores" is incorrect.
There are a few romance languages which use the grammatical structure of "the body part hurts/aches me". But in English the proper structure is "My body part hurts/aches". Where as in those romance languages expressing pain uses a reflexive verb, in English they do not. (the reflexive nature of the phrase is generally reflected in the use of "My", which assumes that the pain being generated affects you. Where as in say, Spanish, "me duele la cabeza" (the head hurts me) assumes the part belongs to you because it wouldn't make much sense for someone else's head to be hurting you. Both structures omit an assumed piece of knowledge that would only be completed by such a phrase as "my head hurts me" but in neither language is that structure ever used.
(I would often make a similar but opposite mistake in Spanish by saying "me duele mi cabeza")