I don’t know what you mean by non-HPV genital warts – that’s a bit of an oxymoron.
1. Does this seem like hsv? Or am I just trying to convince myself? Could these red dots (raised or not) be hsv? Or just warts/ my penis head reaction to the solution?
This does not sound like HSV to me, no.
2 I’ve had shingles before and these are nothing like those blisters.. would hsv blisters be shingles-like?
Where was your shingles? and yes, HSV blisters would look something like shingles blisters.
3. Is it worth going to urgent care today? Am I out of the time window? Should I abstain from sex w/wife?
You could certainly have urgent care look at your genitals. I have no idea if you might have had HSV before this encounter or not, so I can’t address the time window and won’t give advice on if you should have sex with your wife or not, sorry. If you have concerns about skin changes in the genital area, you should have a professional do an exam in person to sort this out. I think your experience presented little risk of herpes but it was not risk free.