I was in the third year of a long-distance relationship with my girlfriend.
Distance is the space between two things, two cities for instance.
Shouldn't it be long-time relationship?
Thank you
It depends what you want to say.
Long distance relationships exist, with couples geographically apart. If the long in this case refers to the time (the 3 years), then I would call it a long-term relationship.
As it stands, it sounds as if they could have been going our for longer and the long-distance part had been three years.