I heard it around 1991. Title could be "Colder Than The Rain" or "Run With Me", but it also sometimes repeats "Goin' Blind". No idea on the artist.
Google claims it's "Naked Rain" from the album "A Violent Impression" (1991) by This Picture. It contains all the lyrics you mention, although technically it's "going in blind".
Wow! You're right! And I already have it -- I bought the disc for one other song ("Breathe Deeply Now"), but I never played the whole thing. Thanks.