What kind of Garden Shrub is this?

I don't know the shrub in the picture, but unless you have a severe allergy to that plant, it was not the cause of that breakout on your arm.... your arm looks like something you carried under your arm, like a piece of a log or a bundle of gr and sticks or some such thing..... hard to 'brush up against' a shrub and have it contact you like that.... get you to a doctor, please... you need major antihistamines quickly......that's an awful rash!!.... I get something like that from cedar and juniper....