First of all RSV is very common and most kids get it every year. That being said, it can also be very dangerous especially in young kids.
My son had RSV last year at 6 weeks and was in the NICU for a week. His oxygen levels got too low and he was working really hard to breathe.
The most important thing is to watch his breathing and make sure he stays hydrated. If he seems to be gasping for air, pulling in underneath his rib cage or at his neck too much or has rapid breathing, don't hesitate to bring him back to the doctor or ER. (More than 60 breathes a minute is too much). The doctors can measure his oxygen level and send you in if it gets too low.
The biggest thing is to trust your instinct as a mom. If you don't feel good about how he is doing, do what you need to get the care you feel he needs.
My son has had chronic breathing problems so unfortunately we have been through this routine multiple times in the past year. It can be scary, but don't feel silly or apologize when you have to call the docs. That is what you pay them for and it is their job to consult you on situations like this. We have had times where we have literally had to bring my son in every day in a week to measure his oxygen levels in an effort to keep him out of the hospital.
RSV generally peaks at 5-7 days from the onset of symptoms and then gets better. Since it is a virus, there is not much they can do for them at the hospital except give the oxygen and check their vitals, which is important if they are doing really badly, but really frustrating to get stuck there if they are doing alright.
Best of luck! Feel free to email with any questions and I would be happy to share more of our experience.
M.