On nights before holidays I tend to let loose and drink a bit more, but when I mix it with tochū tea I don't get any hangover at all.

Literal

Holiday [attributive-の] before [and-など-は] a-little restraint [object-を] remove-[and-て] drink [but-のだが], tochu-tea-mixed [with-で] drink [if-と] hangover [subject-が] completely not-exists-[copula-だ].

Casual health-related observation. 羽目を外す ('to let loose, to go wild, to get carried away,' literally 'to take off the frame/harness') is a set idiom for letting go of restraint — often in drinking contexts. 二日酔い ('hangover,' literally 'two-day drunk'). 杜仲茶 ('Eucommia tea'), a Chinese herbal tea said to help with various ailments. 割り ('mixed, diluted with') is used for drinks mixed with something else.