This sounds
very similar to something I've had twice recently. Pink-ish, bumpy skin on my cheeks - although I also had a few small dry patches. Like you, I struggled to cover it with makeup and it really got me down after a while!
I tried everything I could think of - Sudocrem, Coconut Oil, a ton of different moisturisers, vitamin E oil, avoided makeup up.... Nothing worked. Eventually I used double base gel (15%) which I think you can get in Boots and similar stores. The first time around, it literally cleared up
overnight which was amazing, the second time around it took a few days.
I still don't know what it was, but I think it might have something to do with the cold weather and central heating having an effect on my skin?... That is just a guess though!
Quick tip for using makeup over the area...
If you're struggling to cover it up: wash your face, then use a gentle exfoliating cream, quite lightly. Rinse. Use a moisturiser which will absorb quickly (I like the Vaseline Intensive Rescue Moisture-Locking one, but any similar product will do the job). Then apply a primer (Porefessional is amazing but a tad pricey, there are lots of cheaper alternatives). These steps help to smooth the skin to make it MUCH easier to apply make up to cover up the area.
Hope this helps!