Is there an app that automatically records my glucose monitor because I keep forgetting to record readings in the app?

Glucometer. Usually most of the current glucometers have a memory, so you do not have to record daily. You may consider buying one.
Glucometer can. I doubt that there is an app independent of your glucometer that will automatically import your blood glucose values. On the other hand, there are glucometers that will record your sugars automatically and allow them to be pulled up easily. I'm sure they can be internet linked if they aren't already.