You could well be screwed.
If you bought non-refundable tickets then that was your lookout I am afraid. You would have had the option to either choose a higher fare with flexibility or use another carrier whose product suited your requirements.
If there is a very good reason you can't travel then the airline may show some discretion (e.g a death in the family etc) but otherwise you will be at the mercy of your travel insurance which you may not even have bought yet.
Airline tickets are generally untransferable (ie. no name changes). Depends on the ticket types and how close you are to departure. Very likely to be prohibited within a certain timeframe to stop intermediaries brokering airline tickets.
Of course I do not believe you have been screwed maybe mis-sold – did you buy on line? Where the T&Cs disclosed at time of booking/sale etc?