A "drogheria" might have been a place where you could have gotten drugs in the olden days, but it isn't anymore. "Drogheria" in this case is a false, not a true, "friend" in that it looks and sounds a bit like a word in English, but doesn't mean the same thing. Today, a "drogheria" is a kind of old-fashioned mom-and-pop little dry goods store, rather hard to find in Milan these days.
There's a nifty one in Milan with an address on Corso Magenta, but with the entrance on Largo d'Ancona.
Why is it so nifty?...More......
Because, besides having a little bit of everything any self-respecting supermarket has (deoderant, house cleaning supplies, shampoo and the like), it also has candy-by-the-pound, teas and...drum roll, please...even some not-easy-to-find exotic food, such as various kinds of chutneys, English cookies (called "biscuits" in UK English, thank you very much), Chinese rice noodles and the like.
The place is called "Grossi" after a family name, but don't look for that on the store front.
All you'll see that is prominent are the yellow and red "J&B Scotch" signs, liquors and wines also being sold here.
Interested in more info about this and other exotic food stores I've found in Milan (no easy task)?
Go here, and download my (occasionally updated) list: https://sites.google.com/site/starsthisandthat/home/my-milan-italy/eating-and-drinking-in-milan.
Forewarned is forearmed. The place is teentsy, and so half the store ends up behind the counter, or way up high, or behind glass doors, so you'll have to ask for help. In fact, within seconds of coming in, you'll be asked "Posso aiutarLa?" (May I help you?) or "Ha bisogno?" (Do you need something?), or something of the sort. So this means you'll get good service, and hopefully will find what you want, but there will be no price and product comparing.
If you're ready to jump into the purchase of your favorite kind of chutney (etc.), a simple "Sì, ma parla inglese?" (Yes, but do you speak English?) will get you started. If you just want to look around a bit, "Vorrei dare un'occhiata prima, grazie" (I'd like to look around a bit, first, thank you) will do.