Don't forget to consider what your dad wants. While relatives can indeed offer great emotional and moral support, sometimes visits can be a big burden for a patient who really doesn't feel well and needs all their strength and energy to be devoted to getting better.
Keeping that in mind, I would let people know that he is ill - tell them what you've told us - that he's pretty sick right now, that he's getting treatment, and that until he's had time to fight the infection there isn't much else to report. Also tell them that he either does or doesn't want visitors according to what he says, and ask them to respect his wishes.
Once family and friends are informed they can make their own decisions about making the trip, or choosing to check in via phone, email, etc. Don't be afraid to tell them about other things they can do to help, so that you aren't left shouldering this task all alone.
Make a list of questions for the drs, too. Doesn't have to be fancy questions - just when a question comes to your mind, write it down, and ask the dr when you see him/her. And write the answers down, too - that way you won't be overwhelmed by stress.
Sincerely,
Tre