Pete is right. Plantar injuries are frustrating and I would add somewhat mysterious. But I do know the longer you let it go the longer it takes to recover. If it hurts when you get out of bed in the morning it might take even longer. I also know that hoping it just goes away on it’s own is a non-starter. So you are right to be asking now.
My advice is yes, you need to lay off and Pete’s recommendations are good. If you are worried about losing aerobic fitness there are other things you can do like biking and rowing. They aren’t the same as running but you can still build a good set of lungs. The actions taken that have helped me include: No more walking around barefoot or in sandals. That spring on the bottom of your foot needs support. I used drugstore supports like Dr. Scholls in all my shoes. Ibuprofen helps for acute pain. It has also been my experience that my calf muscles are beyond tight so foam rolling is good but getting someone to work those things is a great help. Increased mobility of your Achilles tendon is also needed.
Be patient and think of it as a time you can do all those shoulder exercises you never seem to get to.