You should not be building everything using only Nand gates. You should be using the parts you have already built in later parts. Think of then as tools; starting with a hammer (rock?) you can build more tools, and every tool you build goes in your toolbox so that you can more easily build more tools.
Your Or circuit does compute the Or function, but it is more complex than it needs to be. Build the truth table for upper input of the final Nand.
That upper circuit can be built using Not and And. Congratulations, you've just found one of De Morgan's laws.