There is nothing wrong with wiping over a bandage if there is a necessity to use and taking it off will harm you.
You should not take off the bandage which is over your wound, especially since taking it off will harm you and make it bleed.
So leave the bandage where it is, and when you do wudu wash the part of the hand where there is no bandage, and for the part where the bandage is, it will be sufficient for you to wipe over the outside of it by wetting your hand with water and moving it over the outside of the bandage.
This will suffice for you instead of washing what is beneath it for as long as it needs to stay, even if that is for many prayer times or for several days.
It is not essential that the bandage has been put on when you were in a state of ablution, rather you may wipe over it, according to the correct view, even if you were not in a state of ablution at the time when it was put on and even if there is blood underneath it at the site of the injection or wound.
