Sick leave when AL denied

Started a job at a soul-sucking call centre a few months ago. Have had zero check ins with the manager (they work remote). Don't always get a reply via email/teams. Had a few miscommunication issues because for some reason they refuse to respond to emails and assume whatever.

I applied for 2 days AL that was denied. I was told I had to speak with them before I applied. Which sounds reasonable but they don't always respond to emails/messages. I never know if I'll ever even hear back. Plus, the workload has been very bad, there's hardly a minute to breathe, let alone any time for emails.

They told me they couldn't approve because it wasn't enough notice and it was during a blackout period. However, other people have had leaves approved. They told me I may be able to log off early on one of those days depending on the workload, but I know for a fact that they are not going to approve this as the workload is insane.

I am planning to call in sick on one of those days as I need the day off. I will get a doctor's certificate. I am worried that the manager will retaliate.

My experience so far has been that the leadership has zero management skills, the team is very disorganised and short-staffed. Incredibly rude coaches/manager and I feel like I'm walking on eggshells.

I'm very anxious by nature and not sure what to do if they retaliate. Obviously trying to jump ship but might be stuck in this role for a while :(

How do people respond to situations like these or deal with leaders like these? I know call centres are not flexible by design but the level of micromanagement is driving me insane cause I can't even pee in peace 🙂