I truley understand your concern. I had a very nasty flu and wondered if that Hong Kong virus is what I really had I was ill for 6 weeks. I was so afraid of passing sickness to my chins. From what my vet told me our viruses are not able to be passed to chins BUT the secondary bacterial infections we contract are transferable. The best way to prevent your chins from bacteria is washing before handling. If you are ill don't spend alot of time with your chins and do not kiss the little cuties either.
As for the supplement to build up the imune system. You don't need to fix what isn't broken. To much vitamins is dangerous so please be cautious and check with your vet before using anything.
I hope for you to keep good health.