If your mom is mentally ill and won't get help the best thing you can do is to try and listen to your mom who's mentally ill and validate your mother's feelings and gently express any concerns you have to her and try to encourage her to seek any help.
You could offer to accompany your mentally ill mother to a professional or research therapists together.
And if your mother is in immediate danger to herself , then you can contact a local crisis response team such as through 988 or in emergency call 911.
In Florida there's a Baker act that can allow the police to temporarily commit someone to a mental hospital for a short period of time.
However if a court deems it necessary to hold your mother longer then they can do that.
However only contact 911 or consider the baker act if actually necessary as it can in some cases make things worse.
But your state has no baker act it can sometimes be hard to get your mom some mental health help when needed if she refuses.
Without a court order or a baker act you cannot force someone including your mother or father or other adult to get mental help.
As adults we all have rights and are ultimately responsible for making or own decisions, which includes when or if we choose to seek out any help or when we feel unwell.
You can't see a health care professional for someone else or force them to go to mental health without a court order or unless they are a minor or are baker acted.