So long as the rash is being treated properly ...

I have a rash in a similar 'embarrassing' spot. I'm also on Warfarin. That needs monthly checking, and Dr Emily has to cross-check all my Rx and over-the-counter stuff for interactions. There's a weak interaction between the rash drug and the warfarin, so Dr Emily asked the 'coverage area' for the jock-itch cream.

I said "Ever see a guy about to get hit?", and made my hands 'assume the position'...

My rash doesn't hurt, but if I am so unwise as to scratch, the relief has the same intensity and longer duration than, well, orgasm. I don't think anybody wants to watch ...

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You were in pain, and I bet also very frustrated about it. Crying is what people do when overloaded by either. It's just human.

Also human, is to apologize when (we even think) we have hurt or inconvenienced someone.

Heck, people have even apologized for "inconveniencing" the medical ambulance team taking them to Emergency Room/Accident and Casualty.

You just had a couple of perfectly OK reactions to high-pain/high stress events.
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The follow-up needed, is to tell the rash doctor how bad it hurts, and maybe the treatment needs to be more aggressive. And also tell doc if the affected area is spreading.
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Deep breaths, have some tea. get a good night's sleep.