It is normal for the screw to break after a few months.
See your Orthopedic Surgeon. He can remove the ends of the screws through out-patient surgery. If he is of the opinion that the screw should not have broken, then you should consult with a personal injury attorney in your area.
Unless this has caused some extraordinary injury due to the screw breaking, you will not likely have a claim.
No, I am not a doctor. Just a guy who suffered a tib-fib fracture and still has the broken screw inside the leg.
The most important thing now is to get your own medical condition stabilized. Whether this is through your own physician or another healthcare provider is up to you. After that, you should get a consultation with a medical malpractice attorney. Medical malpractice requires more than an unfortunate medical result, but requires expert medical testimony that the care that was given to you fell below the average standard of care, and that the below average care caused you harm.
This answer is offered for informational purposes only. It is not offered as, and does not constitute, legal advice. Laws vary widely from state to state. You should rely only on the advice given to you during a personal consultation by a local attorney who is thoroughly familiar with state laws and the area of practice in which your concern lies.