I need to know what kind of lawsuit to file against an insurance co. that is lowballing me. They say my medical expenses should be lower.

I assume you are talking about the other driver's insurance company. This is a 3rd party claim and his carriers regards you as the enemy and will continue to low ball you until they wear you down and you accept or are smart enough to see a lawyer; by that time they will have gotten you to make so many concessions and statements that they will have weakened any possible case you would have had.

If your own carrier acted in bad faith you could have a claim against it for bad faith (which requires a lawyer to bring if you expect to succeed) but hardly any states allow bad faith claims against a 3rd party's insurance company. (I am NOT a NM lawyer so I can't say what that state's laws and rulings provide in that regard.)

No insurance company willingly offers lots of money. It always questions medical bills that appear excessive. Pain and suffering is something a jury awards or a lawyer gets for you. It's well neigh impossible to get an insurance company to offer it, and they will not pay it to a person foolish enough to represent himself in a significant accident except in the rare case where they know that by offering $X as "pain and suffering" or for "inconvenience" they likely would be saving 20X in other damages the poor fool doesn't realize he could have received for future consequences and harm -- because when the case is settled they get you to sign a general waiver as art of the settlement.   

See a lawyer who specializes in auto accidents or personal injury before you damage up your claim some more. They work on a contingency fee and get paid after they recover money for you. If they don't think they can do far better for you than you can do on your own, they would likely tell you that.  www.AttorneyPages.com is the place to find good auto accident lawyers.