The sentence you wrote is almost correct, but it sounds a little unclear because it says 'like me' without specifying who 'me' is. To make it clearer, you can say:
"Cells like these make up your brain and nerves."
Here, 'these' shows you mean the cells you are talking about, and it makes the sentence clearer for everyone. Another way to say it, if you want to include yourself, could be:
"Cells like me make up your brain and nerves."
(Only if you are pretending to be a cell!)
Both options are good, but remember to be clear about who you mean by 'me'!