Yes, your travel insurance should cover you. The travel company you have booked with should provide you with written notification of your cancellation of the holiday which you submit to your travel insurer. The insurer will probably request a letter from the hospital/doctor stating that you are unfit to travel.

In the circumstances, wouldn't it be better for you to claim for this against your insurance anyway, get your money back and then rebook once you know that you definitely have the all clear to travel? If you have an annual policy then you are going to have declare this anyway and possibly pay an additional premium for cover given you have been hospitalised. And if you had single trip insurance for this holiday then you are going to have to take out another policy for the re-arranged holiday anyway, again declaring what has happened this time. Either way, you might as well get the benefit of being insured for this trip - after all it's the reason for taking it out.

I can't really add much to what Judith and Sma have said. I have recently had to cancel and claim through insurance. It was pretty straightforward ( had been dreading it!)
Assuming that you have declared everything on your insurance, as you will need to submit a form from your doctor. You then need cancellation letters or emails from the companies you booked through.
Your insurance company will guide you through this. It's very straightforward.
Then you can wait until you are fit enough to enjoy a holiday. Obviously insurance will be a bit more but shop around or ask on here when you are ready.