Sounds like you’re legs are pretty cooked right now and severe, prolonged muscular fatigue is one of the signs of OTS (overtraining syndrome). I doubt the doc will help you. Docs are used to treating sick people. Even in your deeply fatigued state you are still healthier than 99% of the the doc’s patients.
Ski touring, at least what you have been doing, is often now easy Z1 training. Read this to understand why. https://uphillathlete.com/forums/topic/big-days-of-ski-touring-still-base-building-or-me/
HR is not the best indicator of strength training type efforts.
You need big time rest and and very light recovery level (HR less than Z1) exercise on flat ground and doing alternative exercises. Swimming would be a good choice. Depending on how deep of a hole you have out yourself in this could take a week or it could take a month and, believe it or not, you may feel this fatigue for several months.
Start resting TODAY and be serious about it. You have been presented with a very valuable learning opportunity here about proceeding with training when your body is telling you to back off. Don’t waste it.