What type of lawyer should I be looking for?

Location: NH-USA

My company uses Venture Insurance Agency as a broker for health insurance for the employees.

I recently found out that the broker company has not made a payment to my insurance since January which has now led to my Insurance being terminated.

I have all my paycheck stubs showing that my insurance payments have been being made with every paycheck.

My HR has reached out to Venture to get the matter resolved and by the emails I can see, we are being given the run around, told the matter is being escalated every time we contact them.

Now while all this has been going on, I have recurring heart issues that require me to see the cardiologist frequently as well as pick up medication. In the time between when they last paid and today, I have now racked up just under $12,000 in medical bills that were previously (mostly) being covered by insurance.

To date, I am out that $12,000 plus the total amount of weekly payments I have been making every week.

What type of lawyer should I be looking for to consult? I am located in NH and I believe the corporate office for Venture is located in Michigan.