It is my understanding that it is correct to use "and me" in a sentance as long as it can be taken out and the sentance still makes sense. Example: Jerry and me went to the store to by ice cream. Is this correct?
No, you have it backwards. You take out the other person to see if it makes sense.
I went to the store.
Jerry and I went to the store.
The clerk gave me a free ice cream.
Th cleark gave Jerry and me free ice cream.