Hello Hela, a cheery good evening to you.
Actually, I wouldn't say either. I'd say:
1. I drank myself into debt.
"Debt" is countable in the sense of individual debts; but you can also call the accumulation of all your debts "debt", at which point it becomes uncountable.
2. I drank myself into debt, my wife left me, the building society repossessed my house, I lost both legs in a car crash, and then my dog died. But that's ok. I don't complain. Win some, lose some. Tomorrow is another day. There's always someone worse off than you. It's an ill wind that blows nobody any good. There are good times just around the corner.
(No particular relevance. I just felt that the forum needed a bracing example of stoicism in the face of extreme adversity.)
Student or Learner