When people talk of killing themselves, it is a cry for help. I've suffered from depression and even went the suicide route when I was 21. Thank God I did not succeed. She needs to see a doctor who knows what he's doing. My mother had the same feeling in the back of her throat. Her doc kept telling her there was nothing wrong. She finally went to a different doctor and they found out her thyroid was pressing into her throat. Maybe your mom just needs to see a different doctor. Sometimes we keep going to the same one because we are comfortable with them. But it's not good when the doctor becomes complacent with the patient. Not saying that is what is going on, just that maybe your mom needs to get a second opinion.
I will be praying for you and your family.