A word of caution, agreeing with MissAdventure. The arrangement LtEve has described may work well informally for her family BUT there is no back-up.
You really do need to go through an agency if you need anything more than LtEve describes. You need, as MissAdventure says, staff who have been trained and insured, with a formal complaints system, and holiday / sickness cover.
My parents insisted on informal care, cash in hand, because they trusted the person who had been their cleaner for years. Although a kindly and honest person, she really didn't have much clue, and was always taking time off to support her own family (in which case, guess who got called!).
PS: hallucinations are a very common side-effect of UTI (mor than with other infections it seems). Depending on how long he has been taking the antibiotics, it may mean that they are haven't yet kicked in (24-48 hours) or they are not working.
Good luck