Does Exercise Increase Blood Sugar Levels.

Yep. Totally normal and not unhealthy because your body will bring that sugar down.
When you do something intense for a short time, your body produces glucose to meet the immediate need for energy to the muscles.

It is counterintuitive and different exercise e.g. a long and steady walk/cycle/jog would lower your bg.

The good news is that just using the muscles more will make you more insulin sensitive and ultimately less insulin resistant especially in combination with lchf.

Two things happen when we exercise
- we release glucose into our blood to give us the energy
- we become more efficient at using insulin
It is the balance between these which determines whether our bg goes up or down.
Generally (but not always) lo ger sustained exercise causes a reduction and stop start causes a rise.
As we have released glucose, we have less reserves which often results in lower bg over the next 24 to 48 hours regardless of the short term impact.

I believe it can. I've noted a rise after a hard cycle ride. This article may be of interest :
https://www.diabetes.co.uk/diabetes-and-sport.html