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I am sorry to learn about your fall and your broken back, I do hope that you are recovering or recovered.
Unfortunately with airline tickets (just like other goods and services that are purchased), you are going to be governed by whatever refund or insurance terms are provided at the time of purchase.
You say in your post that you did not purchase travel insurance, so we do not need to examine that issue.
The refund issue can be a little more complex, again this depends on what the exact terms the airline offers (not all airlines offer the same terms, and not all tickets sold by the same airline have the same terms or conditions (for example tickets purchased on a promotion price will usually have different terms than those purchased for premium or advance rates) - so you need to identify the terms that apply to your ticket).
You can find the refund policy for your tickets by reviewing your ticket receipt (if you purchased online, or received an email copy, this will usually be sent with them, if you cannot find it, contact the airline's customer service and ask them for a copy of the terms and conditions attached to your tickets).
Most airlines that do offer refunds for non-insured tickets will do so under some variation of this: charge the passenger the full cost of the ticket, but allow the customer to apply the ticket price to a future ticket minus a service charge. (So it is not really a refund in the sense that you get your cash back, but rather it is more closely akin to a "store credit" with the airline minus a service charge).
But again, you need the ticketing agreement for your specific ticket in order to determine your exact rights in this situation (as well as how to go about enforcing them - such as how to give notice to the airline that you are exercising your refund rights).