1. Get everything in writing
2. 40% contingency sounds high. 30% is traditional, but expenses on top of that could come out to 40% total.
3.  You didn't mention auto damages so I am assuming those were not part of the settlement.  If you had either collision or unisured motorist coverages and the other driver's insurance refused to pay, then your insurer would have been responsible to pay for the damages and then it would seek reimbursement directly from the other driver's insurance.  In other words, at least for the auto damage, it would have been an argument between your insurer and the other parties insurer and you wouldn't have to be involved.  (at least, that has been my experience in just a couple of fender benders)

4. Medical coverage is may be different and probably differs from state to state, but it seems to me that if your insurer was going to claim proceeds from the lawsuit, they would have had to been part of the lawsuit since your obligation to them is only up to the amount of your deductible.  Not clear from your description if this was the case.

5.  I am not an attorney, but it seems to me that the settlment should have had some stipulations has what the settlment amount was intended to cover, e.g., medical expenses, lost wages, etc. etc. and whether or not pain and suffering was one of those items.