I had the J&J shot in mid-March. Yesterday I went to my local CVS for the influenza shot and they were taking walk-ins for the Moderna booster. (Walk-ins accepted every day except Sunday). So I got both - one in each upper arm.
This morning both arm muscles are VERY sore, with the one that got the booster being worse.
And the other side effect is a feeling of wellbeing and calmness. It’s wonderful.