How do you write this in a sentence Jimmy and I or Jimmy and me?

It depends on the rest of the sentence. Take out the words "Jimmy and I" and say the sentence using both 'me' and 'I'. Which makes sense?

For example, let's say the sentence is, "Jimmy and I went to the store." Take out the "Jimmy and I" and you are left with either "I went to the store" or "Me went to the store." Obviously, "I went to the store" is correct. You would not say, "Me went to the store." Therefore, in this example, the proper usage would be, "Jimmy and I went to the store."

But if the sentence was, "She is coming with Jimmy and me." Take out the "Jimmy and me" and you are left with either "She is coming with I" or "She is coming with me." In this case, "She is coming with me" is correct. Therefore, in this example, "She is coming with Jimmy and me" would be the correct usage.