You would preferably want to use a landing page of your own to track incoming traffic from your Adwords campaigns.
And ask your affiliate manager if they can hook you up with a tracking pixel.
Some software available that you can use to track conversions:
KeywordXray
Keyword Radar
XtremeConversions
I can't vouch for these programs and i don't know how safe they are, that is if they use your data for their own benefit.
Here is an
tutorial that explains how you can set this up on your own, it seems complicated though.
For some good info that can help you with your current and future campaigns i recommend to read this:
MindValleyLabs and this
source of valuable information.