According to the studies I read the hsv1 responds well to THC. So any strain (all MJ has THC)
There are many strains that fight inflammation and one of the top of the list is Critical Mass. CM is an Indica Hybrid that is high on the inflammation list, but because it is an Indica it can relax you a bit too much and isn’t really considered a daytime med.
For daytime use maybe a mix of the Critical mass and something like Amnesia Haze which is a Sativa. That way you can still get the job done. Consider infusing s lip balm to get the meds right to the sores as well!
Hope this helps!