Please tell me which is correct

...my brother and me.
My brother and I . ..

In this situation always look to separate out the two parts - 'I' / 'me' and 'my brother' in this case - and deal with one at a time. Which would be correct?

I ...(did / saw / ate etc.)
or
Me ...(did / saw / ate / etc.)
???????

That should give you the answer. However, you would sound more natural saying 'My brother and I...'

I should add, I'm assuming you're using your phrase as a subject of a sentence - if not, use the same technique of one part at a time.

It was given to ( I / me ).
Which would work?