The devotee does both. He/she lives as normal as possible, and at the same time, strives to serve God well.
In your situation, it is good to see that God is manifesting in your illness, and also in the doctors and the hospital. Explore all your options, and at the same time offer them up to the Divine. You may read more and saturate your mind more with heavenly ideas, if you can. Should you have to go to hospital, then cultivate the feeling of acceptance. God never gives us more than we can bear.
'Try to do as much as you can in the remaining short life span?' If you are referring to spiritual practices here, then this will help you. Everything else is useless.