I've never had to deal with breakouts on my skin but ever since I started getting laser hair removal on my face I've had a few breakouts and I've had to learn whats a quick fix.
1. Mario Badescu Drying Lotion $17
-Never shake it, just use a q-tip and use on blemish
2. Bee glue/propolis $16
-I know this sounds weird but bee glue comes in a jar and separates like oil. You apply it to your blemish at night and when you wake up, voila. It is magic.
3. Tea tree oil $11
-The classic remedy to use right before bed (comes with a dropper too)!
4. Lavender/Camomile Oil $14 - $25
-These both soothe, so these are great for red pigmentation
-Use toothpaste this is like an old wives tale used to dry out the blemish. First off, there are products out there that do the same thing which are more effective. But just take a look at the ingredients in your classic crest toothpaste (It's a little horrifying). There are unspeakable chemicals in it that you should not be putting on your face. Use one of the products listed above instead.
-Also never try to conceal a blemish. Why? First off, concealer is used to brighten, that's why you use it under your eyes for dark circles. If you use it on your blemish it will highlight that part of the face and draw attention. But you also just want to leave it alone! Don't use any additional or harsh chemicals because that won't help it, instead opt out for one of the remedies above!
I use these all at night so it has enough time to be set. The list is organized by the most extreme to the more mild treatments. Hope this helps!