I agree with your sentiment
But I look at some aging YouTube mechanics, and my dad who was in the business in the 70s-80s
And I get concerned about long term chemical exposure
Older mechanics all seem to have the shakes (watch their hands)
I'm told the chemicals that used to be in brake clean caused it, a long with some nasty cancers
Nevermind the asbestos, and the general carcinogenic greasiness of a shop setting
I'm taking PPE more seriously these days, and I'm only buying non chlorinated low VOC brake cleaner
As to your particular series of events, probably more an issue of breathing it in than skin absorption
Maybe use a little less next time, or in a more well ventilated area