Soon after cameras were invented, there was a great effort made to get cameras into everybody's hands. Those who could not afford a camera outright would buy points at 1/100th the cost of the camera, to be pasted into a book much like US Savings Stamps, which only USn old timers will remember. The Brownie points could then be redeemed for an inexpensive Kodak camera called a Brownie, hence the term brownie points.
Brown-nose is a derogatory term derived from the fanciful idea that a Pinocchio-like person would lie so much and kiss the boss's ass so much that his nose would be turned up until it met the kisser's forehead. Hence brow-nose, which soon became brown-nose.
Actually, there isn't a word of truth in the foregoing two paragraphs. Except that Kodak did make a Brownie camera. There's still one floating around in our family, belonging to one of my brothers. A simple box camera that used either 120 or 620 size film, I think the former.
Brownie point according to the Dictionary of American Slang, which is sitting open on my lap, is defined as "[from the point system used for advancement by the Brownies of the Girl Scouts but strongly reinforced by BROWN-NOSE]. a credit toward advancement or good standing, esp. when gained by servility, opportunism, or the like."
In the same source, brown-nose is "[of scatalogical inspiration but now considered vulgar} Originally Mil.(itary) a toady; an obsequious sycophant." This dictionary gives a 1938 citation followed by a host of others from the 40s and 50s.
