My company closed its doors in Dec 2016. Can I opt out of the search for jobs if I have cancer?

Hello, In December 2016 the company I had worked for since 2007 closed it's doors. It was a great company and my job was part-time 20 hrs per week. In 2014 I was diagnosed with Cancer and had 6 months of Chemotherapy. I still worked 3 weeks of each month and the owner was fine with my hours. When they closed the doors, they told me to file for unemployment, and I did. But the problem is, I don't want to get another job right now because I have no Immune system because of the Chemo and I have to have one day a month to go into the cancer center and get an infusion of Immunotherapy. I don't think I have the strength to begin a new job anymore but I still need the income per week that UI is giving me. I am 73 yrs old. Can I get out of the search for 3 jobs each week and still get benefits??? Thank you!