I’ve had what I think is a cold lately, and been blowing my nose a lot. That means, of course, that the rim of my nostrils, especially at the bottom and inner edges, are raw and red. Any advice for relief?
Chapstick or other thick lip balm. Warning: do not use any lip balm with mentholatum or mint in it. It’ll burn like a mofo on a raw nose.
Hand lotion. Applied after every nose blow. Or, if you’re all fancy 'n stuff, the tissues with lotion built right in.
Yeah, I have used Carmex to good effect.
Treatment - non-menthol chapstick, lotion (preferably unscented, because… nose.)
Prevention - if you’re all fancy, lotion-infused tissues. If you’re cheap like me, unscented baby wipes.
Wash the affected area with plain warm water frequently. It’s the mucus that’s irritating the skin.
I use Bag Balm, the smelly stuff in the green can, mainly for this. It works for me in a matter of hours. 
Little dabs of Vaseline work for me.
Same here…
Aquaphor on the chapped nose. It doesn’t soak in as quickly ask vaseline, so it protects longer.
And buy lotion tissues to use for the rest of your cold, and to keep on hand for the next one.
After a particularly bad allergy season, I found something I think works even better than Chapstick or Vaseline: Vitamin E Oil. It’s both soothing right away (no burn)and feels like it helps things heal faster. Make sure you put it on overnight.
Before that, I usually used Blistex Medicated or Vapo-Rub. I like the burn. 
Also, absolutely get the lotion tissue. Puffs Plus brand is hands down best in my opinion. And wash regularly to remove the irritating mucus.
I use a topical anesthetic antibacterial creme, like Neosporin. I figure that a nose rubbed raw is pretty much an abrasion. I put Neosporin on a few times a day, and things often start healing before the cold is done.
As above the petroleum jelly. Also, use a neti pot. Also, stop scraping the tissues across your nose, dab gently.
Medicated Chapstick, which contains petroleum jelly.
Get yourself a big pack of Boogie Wipes. They’re really gentle wipes with just water and saline on them and are made for exactly this purpose. You’ll find them in the baby aisle with the diaper creams and such. Trust me. They’re a life saver.
I’ll also second the recommendations for Aquaphor. Combine the two and you’ll be set.
My experience is the best way to cure a raw nose, and upper lip, is not let it develop at all.
Here’s how I do it, I don’t use paper tissues for nose blowing, I use cotton handkerchiefs, or at home I use old pillowcases cut to usable size. The raw nose has never developed using handkerchiefs. The benefit is that you will also find your colds and allergies will not be as severe and go away faster.
I know that this is violating a cultural taboo, but really, the paper tissue industrial complex has somehow convinced people that it’s ‘more sanitary’ to use ‘one time’ tissues. I don’t buy it, and I’ve found that throwing used handkerchiefs in the wash with hot water and soap is worth the trouble.
I have a theory, that the cellulose fibers actually irritate the skin, and when you use them to wipe your nose, that tiny fibers get inside the nose and irritate the nose and make the cold last longer, or act worse.
I fell into this when I had a dog who would eat used tissues, so when I had a cold I switched to cloth handkerchiefs in the form of cut in quarters pillow cases. The dog wouldn’t tackle those. I noticed I didn’t get raw noses and my colds were cut in half.