I have a similar problem with exercise, whether it is weights or cardio, and no matter the time I do it. During a long work-out with cardio only (45 minutes), I will lose about 80-100 points on my BG. Within 10 minutes of stopping the exercise, I start climbing again, and rapidly. If I am low at the end of the exercise, but not lower than 55, I will not treat the low, because I know that 100 points is coming back, and quickly.
The drop in BG with a weights work out is not as pronounced, but the post work-out rise is the same.
As a pumper, to counter the rise, I start a 125% temporary basal for twice the exercise duration a little bit before I start the exercise. I have about a 90 minute delay from when I take my dose to when it starts to have an effect, so I hopefully am timing the increased basal to kick in when the exercise ends. It does not work perfectly, but it does.
There is also the “dawn phenomenon” at work possibly. You may be going up just because that’s what happens to a lot of us in the morning (just another reason to sleep late, in my book).
Also, you may be getting the effect of the late digestion of your protein shake without the insulin to address it, since you do not take anything with the shake. I used to use a protein shake that had 7 grams of carbs in it and would go up a huge amount (with or without exercise) compared to what happened if my carb ratio was working. It was too hard to figure out what to do for that particular shake, so I gave it up.
I would not go without some insulin for your protein shake – humalog may not be right, because it will peak too soon, but you should probably have something.