Hello and thank you for contacting us. This is Dwayne B. and I’m an expert here and looking forward to helping you today.
You absolutely could have a bad faith claim against your insurance company or, if not bad faith, at least a breach of contract/duty.
Most insurance companies won't settle a claim for policy limits without a complete examination of all of the medical records, a physical examination by an expert PLUS a full release for their client. They almost certainly could have gotten a release for if they were willing to pay $100k and the Plaintiff is only asking for $25k more.
You probably want to visit with a lawyer that does this specific type of work.
You can find a lawyer to assist you by going to www.lawyers.com and in the section for Area of Practice enter Civil Litigation or Consumer Law. Either of those will have the skill set you need.
If your question has been answered then I'd offer my best wishes to you and ask that you please not forget to leave a Positive Rating so I receive credit for my work.
Of course, please feel free to ask any follow up questions in this thread. I want to be sure that all of your questions are answered.