Anything up to 11 is 'normal'....
The home testing kit you have is accurate to within 10% or so, it's as accurate as they can make them.
So a reading of 11 is high, but doesn't mean he's diabetic.
Those readings are high, but only on the high end of 'normal'. His body is bringing those readings down, which is good.
Blood sugar readings get higher in everyone when they're ill, as our bodies need more energy to fight infection, fever etc.
Keep in touch with the doctor, see what the test results say. The big sign of diabetes to watch out for is a really increased thirst, when i was diagnosed, i was 9, and drinking 12/14 litres a day.
It could be many things, so keep on the doctor, make sure they explain all the tests, what they think it could be etc.
Best Wishes.