accident europe

I was working abroad where I was a passenger in a road
traffic accident that was the fault of another driver who seems to have
admitted responsibility. I work for a company via an employment agency. I
have a few questions linked to this incident and would appreciate any advice
anyone has to offer :-)

I have received letters from the hospital over there, billing me for the
emergency care I received immediately after the accident. Do you think I
should pay for this now and then try to obtain a refund from the insurance
company of the driver responsible or should I approach the company I work
for to check if the travel insurance they should have taken out on me covers
these costs?

Also, could anyone recommend on the steps I need to take now to resolve this
issue most effectively - this is all new to me as I have never been involved
in a serious accident and never needed advice from a solicitior.

Yes check with the insurer first by all means.

WLD lawers in Europe could also become directly involved if need be.