Are you sure about the age of your conure too? Conures go into sexual maturity between 9 and 18 months, year about average. And while there is always talk about the larger birds and how they get hormonal, in all honesty, conures go nuts, its not very often to find a conure that isn't a real handful during the 9 months to about 2 year age range. Just something you gotta suck up and work thru.
But, presuming its not just coincidence that your conure is upset about another bird being in the home, only being there 3 months, may not be as confident in their place in the flock, so feeling quite upset about another bird. Or as many conures are super social with all family members, there has to be some change for the conure with another bird coming into the home. Only so many hours in a day, so even tho you believe you are providing the same time and attention, chances are its not the same for the conure. Provide extra toys and activities to teach your conure independent play too, but start some easy training if you haven't already. Something like target or touch training, super simple and its just focused one on one with your conure. The biting and nipping, well, its a precursor to puberty so start working with that now. Redirection, stick training, reward for stepping up without using the beak. I'm guessing there are lots of threads in here too

But, having 3 conures in our home personally that we had from very young and thru puberty, the nippy stage is a just push thru it type of problem. I also have the great fun of being the person that gets to work with and rehab many of the 'problem' conures that come into the shelter. I have only had 1 failure in the small birds I've worked with, and often with this type of behavior its either straiht up hormonal, anger or jealousy problems. All can be worked thru with time and patience. Start with positive reinforcement for good behavior, but don't ignore bad behavior. Remember that conures are very closely related to macaws, so when you hear about getting all the big bird personality in a tiny body, there is a lot of truth in that statement
Best of luck in dealing with both babies!