Boldyloxx and Wrenn gave you some great suggestions. Tons of natural antibacterial and antiviral things out there to take or apply. Diet cleanup is key.
One other idea: Salt water rinses. You put Seasalt into very warm water, make a salty brine like sea water. Use it to fill a clean sink or bowl. Dip your face into it and keep it in there several minutes. (breathe out gently while your face is in the water. Come up for air, then repeat). You may not even want to rinse.