In order for you to get a black eye you guys were probably going at the level that the amateur fighters/pro go at. Hope you had your mouthpiece and head gear.
With that being said you just started three months so majority of the lessons they're going to teach you is offensive then of course eventually defensive moves; parries, guard, leg blocks, catching kicks, and then counters. I'm surprised they allowed you to spar already. At our gym they wait about a year. First time I saw our guys sparring one guy had his head split open, of course by accidental head butt. With blood gushing out he just said fawk it and continued sparring like it was no big deal...lolz!
I'll tell you this though...you'll learn really quick what works and what doesn't if you're sparring at that level already...haha.
BTW: You guys sparring in a ring or cage...