I would relax for now until you actually see signs of an illness. I doubt your other rooster hurt him. We all have ahd chickens just drop dead--it happens.
It is good when you want different breeds and have a rooster of each, to keep the hens together in a flock with one rooster at a time. You only need to separate the hens with the one breeding rooster in a breeding pen for the season to breed and collect eggs, which is usually not that long a time. Keep the other roosters in separate pens with food and water where they have company, but are not close enough to get to each other. You may also rotate the roosters into the flock if you wish, during the non-breeding times.
Everyone does things a little differently, and sometimes it takes some experimentation to see what works for you.
It is good when you want different breeds and have a rooster of each, to keep the hens together in a flock with one rooster at a time. You only need to separate the hens with the one breeding rooster in a breeding pen for the season to breed and collect eggs, which is usually not that long a time. Keep the other roosters in separate pens with food and water where they have company, but are not close enough to get to each other. You may also rotate the roosters into the flock if you wish, during the non-breeding times.
Everyone does things a little differently, and sometimes it takes some experimentation to see what works for you.