I came across the following sentence:
I'm guessing it means something like:
You forgot me!
But what is happening / what is the meaning with the
や being attached to
ちゃう's verb stem?
Pretty sure ちゃ is the shortened form of ては. では/ては can be used in a similar way to the conditional たら, but only for negative results. For example:
It will be a problem if you skip work when we are busy.
There are many other ways to use this grammar point, including what you mentioned in the comments.
You have to do it that way.
For your example, if you expand the sentence, it should become:
If you forgot me I would feel bad. (literal translation)
I don't want you to forget me. (natural translation)
いや・嫌 here just expresses that the speaker is emotionally opposed to this happening. So "If you forgot me, I would have negative emotions." I hope this helps :)