The key with side rooms is that you prioritise people who could infect other people - otherwise, before you know it, you have a whole ward infected. However, if someone has no immune system, they also get priority.
Every hospital will have a bed manager, whose job it is to look after the entire hospital bed system. So they will know which patients need side rooms, which patients have D&V, Flu, Sepsis, etc., and whether they are male and female.
If required, they will cohort patients into bays who have similar infections. For example, they could have a C.Diff bay on a ward, which is shut off from the rest of the ward.
Your relative will be having blood tests, which will tell the doctors what level of urgency is used to isolate them. Even on a normal ward, they can do limited isolation, where they shut the bed curtains and people have to glove/gown/mask before entering. It's not quite the same as a side room, but it does offer a small layer of protection.