I got my 3rd Moderna injection this week without any real issues. The pain didn't even last 24 hours. Noticed increase urination about 2 hours after the injection. Nothing like #2 where I lost #20 pounds in 24 hours. I waited until a Nephrology Doctor said it was ok to move forward. Also no lower back pain like injection #1. I know a few people that had that issue.
I also add the flu shot same day.
No side effects with either one.
Don't forget they now recommend getting the flu shot when it comes your time for a booster. There is no interaction and no issue with doing one shot per arm.
Moderna is working on a combination booster / flu shot all in one but it is not approved yet.