Hello,
Understandably so your father may be going through a difficult time given the present situation. If he has a preexisting anxiety related problem, it might escalate in the context of his brother’s death and his health (since you mentioned that he was in the hospital).
Next Steps
Grief therapy is highly recommended as it will help your father better deal with and come to terms with the death and may alleviate some of the related anxiety. A detailed evaluation may also help identify the existence of an anxiety disorder, if any and thereafter, follow a treatment plan for the same involving medication/therapy.
Health Tips
Support him to the best of your abilities and acknowledge his feelings instead of rubbishing them or brushing them off. In the meantime, reach out to a clinical psychologist for help related to starting grief therapy for your father.