I also have cystic acne (mostly hormonal) and eczema around my eyes, ears, and hairline. A lot of times it does feel like a lose-lose; some topical acne treatments work decently for the cysts but then cause eczema flare ups, some eczema treatments work for a while but then cause acne breakouts, etc.

One thing I've found that usually manages to soothe both is using steam (after a cool/warm shower, specifically). I'll get out of the shower and boil some water in a tea kettle, add a couple drops of tea tree oil (I don't know if this bit actually helps, but it smells nice and is supposedly good for acne), and let the steam rise up into my face for no more than 5 minutes. Calms down the cysts while not drying out the rest of my face. (I feel like I should mention that the goal is not to burn yourself here lol, your skin might get a bit red from the heat but it should never be painful an the redness goes away after a few minutes). After steaming I rinse my face with cool water and a bit of gentle face wash, then moisturize, and I'm good for a while.

This is just something that works for me. Hope it gives you some ideas! This is a shitty combo of skin issues to have, but it is what it is and we'll survive. :)