Drowsiness / Sloth & Torpor Does drowsiness as a defilement only refer to a psychological state of mind? I know that emotions manifest also as physical phenomena, but how do I distinguish between physical exhaustion and psychological defilement?

If I am done with my job or school I'm feeling sometimes exhausted. How do I know if I have this defilement in me? Now of course if I ate a lot then it's clearly a defilement.

Just for convenience I was thinking that the next time I'm feeling  physically exhausted I am going to meditate even if just for 5-10 minutes to give myself the chance to have a sense of achievement and well.. maybe the sleepiness disappeared by then.

Any thoughts or sutta references? (I am aware that the Buddha advised to combat drowsiness and if everything fails one can take a nap)
Does drowsiness as a defilement only refer to a psychological state of mind? I know that emotions manifest also as physical phenomena, but how do I distinguish between physical exhaustion and psychological defilement?
Drowsiness depends both on the psychological state and physical state. There is nothing purely psychological or purely physical. Both psychological and physical changes can occur simultaneously depending upon the choices you make regarding your mind and/or body.
If I am done with my job or school I'm feeling sometimes exhausted. How do I know if I have this defilement in me? Now of course if I ate a lot then it's clearly a defilement.
Yes. It is a defilement. It is the lack of energy which is causing you to exhaust quickly.
Any thoughts or sutta references?
Yes. Buddha understood this problem and came up with a great solution.
Please go through what I discovered here.

Furthermore, a mendicant has wandered for alms, and they got to fill
up on as much food as they like, coarse or fine. They think: ‘I’ve
wandered for alms, and I got to fill up on as much food as I like,
coarse or fine. My body is heavy, unfit for work, like I’ve just eaten
a load of beans. I’d better have a lie down.’ They lie down, and don’t
rouse energy for achieving the unachieved, attaining the unattained,
and realizing the unrealized. This is the sixth ground for laziness.

Next he says

Furthermore, a mendicant has wandered for alms, and they got to fill
up on as much food as they like, coarse or fine. They think: ‘I’ve
wandered for alms, and I got to fill up on as much food as I like,
coarse or fine. My body is strong and fit for work. I’d better
preemptively rouse up energy …’ … This is the sixth ground for
arousing energy.

The point is to think positively. Think in what ways now is advantageous for rousing up energy to fulfill the urgent goal of focusing on Buddha , Dhamma and Sangha. The sutta I have quoted covers 8 grounds for arousing energy I am sure you will find the one suitable for you.