Does taking any supplement such as detox tea product have any side effects ?

Depends on the tea. Most tea contains caffeine, which energises you and in enormous amounts (way more than you'll get even from a whole box of tea) can cause halucinations and being even more tired. The herbal tea itself may contain other drugs or substances which can affect your body. And I don't mean to burst your bubble or anything, but detox diets have kinda been proven to not actually "detox" your diet. I recomend eating a balanced diet, which will depend greatly on you, taking in a little more fluids, starting some exercise routines, and if your still feeling yuk, see your doctor. I hope this helps!