Please take all the time you need.
Losing a pet, even in the first few days, is hard, seeing that being die next to you is one of the worst things I can remember.
It will get better with time but it will always be a weird feeling.
The only advice I can give is to live through the next few weeks and then look for another pet. Not as a replacement, because it never will be, but as a new companion to help with the feelings.
Please try not to think that a few minutes might have helped.
Whatever caused her death, if it's so sudden and inexplicable, a few minutes probably wouldn't change anything.
But thanks to you, she didn't have to die muzzled in a cage. It sounds like you allowed her to have a peaceful death instead.
The following may sound dull, but I wish someone had told me this: Focus on the time you've had.
Even if it was only a few days, during those days you gave her a better life.
Belive me, that's is all that matters in the end.
