Yes- a broken blood feather doesn't often fully heal- it's like a fairly dangerous scab because it is basically a funnel to their insides when open. If is bumped or messed with, it can open back up (although they don't always). Since this is the second event where it has opened up, I would consider taking your bird to the vet to have it removed. Yes, TECHNICALLY, in an emergency you could do it yourself (and yes, normally you want to wait and see if they heal first, unless you cannot get it to clot)..BUT, I am wondering if this same feather had begun bleeding again...If that happens at night, your bird COULD bleed to death if the feather doesn't clot...plus, you can screw it up on your own and make your bird mad or squeeze to hard etc---you don't always want to remove a broken blood feather, but when it causes ongoing issues, or if it is bleeding and you can't stop it, it needs to go.
A new feather could not have matured in 1 month's time, so if you think it is the same one, it is probably the same wound re-opening.
EDIT: You say the feather came out, but ARE YOU SURE??? One month is nothing to grow an entire new feather...
I imagine it is not the same feather, but possibly a nearby feather (unless you only thought the feather cam out, and in actuality, only part of it did...)