Hi,
Extremely unlikely (almost impossible) that you would be randomly stopped and questioned based on your caution.
As far as I understand it, you are not eligible for the waiver programme (ESTA) if you have an arrest involving drugs.
I had similar caution and obtained a 10 year visa. I kind of regretted the process since because by all accounts unless you intend to live / work stateside, you are never going to get collared.
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