– Can HSV-1 cause rash as described (both the symptoms, and duration of rash lingering)?
No, from what you’ve described, you have balanitis, a common condition of the head of the penis. Look it up. It is usually caused by a fungal infection.
– Do you know the chance of a false negative on the IgG test if done only 3.5w out from possible encounter?
Probably at least 50%, probably more
– What % false negative might there be if I retested IgG after 7 weeks, and after 12 weeks?
The IgG test misses 30% of HSV 1 infection, even if you wait 3 months.
– In your experience do you have any other recommendations given my symptoms?
Just balanitis.
Terri