Note that you can use it to your advantage too. Bad allergy? Sleep less, it'll raise your corti??? and reduce the effect of the allergy. Not a long term solution, but works well when you are at the pick of it.
Of course, this whole article is based on a really small sample size...I would take it more as a suggestion than a solid scientific result.
Sleep deprivation increase the levels of cortisol which is in part why you tend to put on weight when not sleeping enough. Cortisol is an anti-inflammatory.
I wouldn't be surprised if chronic lack of sleep increase inflammatory, due to some other mechanism, but for sure, short bouts of sleep deprivation has worked wonder for me to stop allergic reactions (I'm talking sleeping less than 4 hours/24 hours period - I usually need between 7 and 9 hours).
I'm not talking about not sleeping well, I'm talking about sleep deprivation, less than 4 hours, when I normally need between 7 to 9 hours.
Also, we are all slightly different, what works for one person might not work for another (we are all an experience of one).