Two things...
1) The insurance company already knows about this incident... if you do nothing then find rot in the future you could be looking at a claim denial. There is flood damage... which you have now.. and there is negligence and subsequent rot.. something that is generally not covered.
2) if water got under the linoleum it will NEVER dry out...
I'm not really going to give you advice on what to do as I wasn't there and didn't see how much water your talking about.
My dad flooded his fiver by accident in the middle of the night (toilet was left running somehow.. just a bit) He took similar action like you did and everything was fine, but he dried out everything he could.
Thanks!
Jeremiah
