Some states' SOL or statute of limitations is 5 years, like Missouri. Some SOL's are 1 year. Consult this web site for the SOL of your state.
Remember, there is such a thing as a "demand package" in which *you* make the first overture to settle to the at-fault insurance company. It is good to note that they owe you nothing. Their insured owes you something. They represent their insured. Be polite yet firm.
You include in this package a letter detailing what you believed happened to cause the accident -- the facts, your medical damages and other damages (i.e., lost wages, etc.) and photos, medical reports, any witnesses and other such things. You can also make an 'demand' that the other insurance company pay you on behalf of their insured X amount of dollars. This X amount should be higher than what you would accept. There are good examples on this web site, as well as other web sites on the net, that show a basic demand letter.
You might ask a PI attorney to also review your letter and give some suggestions. He/she is always an excellent resource to find out where to go from where you are now *if* a settlement is not reached. Attorneys charge between 30% and 40% (or more) if they have to file a lawsuit. And usually that lawsuit never goes to trial. Usually. Settlements are often made before a trial date or sometimes just right before the trial starts. Now you have your attorney to pay on top of everything else....... AND you might get lower than what is fair.
No one can decide for you whether to file suit or not. Unless and depending on the severity of your injuries, you might want to try to settle with the other ins. co. first. It takes real determination to pursue a lengthy lawsuit situation. The other side hopes you will cave in with debt from medical bills or others and eventually just accept anything. Only you (and your trusted attorney) should decide on what is a *fair* settlement for YOU!