I need advice from experienced runners/joggers. (is this normal ?)

I think that you have discovered the cooldown period.

@Nullo See that’s why I asked for advice from “experienced runners/joggers.”
Click the link below and read the last sentence of the first paragraph.
link

* shrugs * I’ve got nothing, then, short of anthropomorphisation of the healing process – that fewer repairs are flagged, so less work is interrupted when you get up. Which is not terribly helpful, I think.
And there’s no reason to be curt. :\

The only thing I can think of is that you are still too wired up and end up having a restless night causing you to be exhausted the next day.
I know after a good work out I need to stretch an do some light activities, giving my body appropriate time to cool down. If I take a shower immediately I will still sweat for a while afterwards, leaving me feel hot and restless.
Your body does most of its repairs at night and it needs to be fully rested.
Also the earlier you work out in the day the longer you have to cool off.
Stretching helps with the healing process of your muscles.
It could also be that you don’t eat properly after your work out or don’t drink enough when you just flop down. You need to replenish what was lost. People who plop down right after tend to neglect their replenishment.
I don’t have that problem but I make sure to work out before 3. If I workout after 3 then I usually will feel it the next day.

So good, already keep healthy, and can finish the work well.

While you are walking the additional 20–30 minutes after your workout you are facilitating flushing of lactic acid (and other metabolic by-products of the work you did) out of the muscles with the relatively gentle movement. Plenty of it will get processed right away. Your muscles will enjoy more flow of fresh blood with all the components they need for repair/healing.

If you just stop it will take much longer to work out the same amount of lactic acid. In the meantime your blood-acid levels are higher than they would have been and that puts a minor toll on the rest of the body making you feel lethargic. The muscles will have been exposed to the lactic acid for longer and they will be more sore, and they did not get the same flow of rejuvenating blood as they would have if you did the warm-down.

I think that your body gets used to being lerthargic and it takes more effort to wake it up.