Corinna/Corinne come from the Greek name Korinne - the e being pronounced and long so closer in sound to Corinna. The Greek root word was spelt kappa omicron rho eta, translates as 'kore' in spelling but the sound of eta was like that of the vowel sound in 'air', more kor-ay than 'kore' or 'kora'. And it had other meanings beyond girl, maiden - newly married woman, daughter, doll, puppet, eyeball and long sleeve - take your pick.
Corinne is simply the French version of the name and the French say it cor-RIN, the e is silent but a feminised spelling in French. That seems very like the pronunciation you give, unless I'm missing where you put the emphasis. I've heard people say cor-REEN but always put it down to regional accents and can't think of any other way to interpret Corinne really kor-RIN-na?
Sorry you don't like the meaning of your name but it could be worse - my name comes from the tribe Dumhnonii whose name meant 'worshippers of the dark god'! LOL - my devout Protestant mother didn't know that when she named me for the area my grandmother came from and honestly I think it's sort of funny.