My mom is a non smoker she has a cough, fevers headaches vomiting only once, body aches and chills does she have the flu? She went to the ER and they told her she has bronchitis they gave her doxycyl hyc100mg and hydroco/apap7.5-325mg but she still feels

Could be flu. If your mom wasn't specifically tested for the flu it may well be that she has it. Given the prevalence out there this time of year.
I'm . I'm sorry that your mom is so sick. She may have influenza, it is certainly going around right now. If she had the flu shot this year then it is unlikely to be influenza. It sounds like the er thought she may have bronchitis, and that is a good medication for that. If she vomits, has fever, shortness of breath, can't eat or drink, or any rash then she needs to return to the er immediately.