Welcome to the Forums, Kelsey, and congratulations on your new and very cute conure baby! Don't forget to tell us his/her name will you??
Green cheeked conures (GCCs) can indeed be a little nippy, and can also be prone to a little thing they call "cage aggression". This is where they come to view their cage and everything in it as their territory and defend it quite vigorously, and often comes more exaggerated when they reach sexual maturity which can occur anywhere between 1 and 2 years of age, sometimes even later. The best way to curb nippiness is to not allow it to become entrenched in the first place. Many GCC owners use the "shunning" method to accomplish this. It involves gently popping the bird down in a neutral spot if he bites you, somewhere like the back of a chair or the floor if safe to do so, but
not back in or on his cage as this may be exactly what he wants! If he flies or walks there himself that's ok, but you don't want to put him back there yourself. You should then turn your back on him or leave the room for a minute or two, making zero eye contact with him. Conures
love attention so he will realise fairly quickly that this biting business will not be tolerated. It is important that every member of your household follows this procedure in order to make it stick - GCCs are also master manipulators and will take full advantage of anyone who is not on board with this method!
Personally I also advocate a wellness check at a certified avian vet whenever a new baby is brought into the household. This is important to establish a baseline of health and to rule out any illnesses he may have picked up at the breeder or from the pet shop, and unfortunately there are a couple of nasties that are relatively common. The following link may help you to find a vet near you if you are not already familiar with one...
It's also good to have a relationship with a bird vet because they are an absolute GOLD MINE when it comes to help and advice with behaviour, as well as having an established health record at their fingertips in the event that your bird has a sudden health emergency.
Other than this, GCCs are delightful little birds and I know that yours will have you wrapped around his little claw in no time flat. I'm looking forward to sharing your journey with him and you
who advocate leaving a new bird in their cage for up to a week to settle in to a new home. I have never personally done this with any of mine and I think you'd quite easily be able to assess whether Clyde (very cute name btw 
