Did they give you a contract with their fee? If not, you don't owe anything..
in life you get what you negotiate.
No win-no fee law suits are weighted in favour of the lawyer but then typically they have a lot of work to do and as you say $10k on a $30k damages payment might seem fair enough. However, for a more serious injury where the payout is going to be greater it might be worth you hiring the lawyer to simply fight the case for you with you paying the bills as they arise. Probably you will end up with a large legal bill, but it won't be anywhere close to a third of $1.45m. Or you could negotiate with the other party yourself - there is no law that I know of that says you must seek legal assistance.
If you are laid up and not doing much then look at similar accidents and at least try speaking to the other party's lawyers. But, bear in mind that any payment you take will be full and final. If you have further problems with the leg down the line then tough - that is why you need a lawyer to make it watertight and to accept the best possible deal.