What you're describing sounds pretty familiar to me because I've seen it in people around me, and honestly there's a factor that a lot of people overlook: sleep quality isn't the same thing as sleep quantity. You could be sleeping those 8 hours but if your body isn't getting into deep sleep phases, you wake up feeling just as wiped out. This happens way more often than people realize, especially with temperature changes in your room, light (even if it's minimal), background noise you don't consciously notice but your brain is still processing, or even changes in your nighttime routine.
That said, yeah, definitely go see a doctor. A month like this is enough time to rule out things like anemia, thyroid problems, vitamin D deficiency, or even mild depression, which often doesn't come with obvious sadness but just that exhaustion that won't go away even when you sleep. Chronic stress also wears you out but in a different way, and in your case it seems more like something physical than mental.
A practical tip I don't think anyone's mentioned: keep a diary for a week jotting down what time you go to bed, what time you actually wake up (tossing and turning in bed doesn't count), how you feel when you wake up exactly (confused? foggy? chest pressure?), and what you eat for breakfast. Take it to your doctor. Doctors understand the full picture way better when they see patterns than when you just tell them "I feel tired". And in the meantime, make sure your room is actually dark (if there's phone light, cover the router, whatever it takes), keep the temperature cool, and don't drink any caffeine after 2 PM even if it seems like nothing.