So the seed diet might be the problem! That's an easy fix! Seed diets are recommended for hardly any birds right now. You should switch him from seeds to pellets.
Some good brands are Lafebers and Roudybush. I have Lukah on Roudybush Maintenance and he LOVES them
Just grabbed the bag and I have the small size ones right now but I've also given him medium size. It kind of depends on which ones are at petsmart the day I buy them.
Seeds are extremely high in fat content and don't give your little guy all the nutrition he needs.
This site has a lot of information on diet for your birdy
Feeding and Nutrition
The best rule of thumb is to have pellets be his main meal supplemented with a cup of fresh fruits and veggies each day, mostly veggies as fruits are high in sugar.
Lukah was on a seed diet when I got him and to switch him over I just took out his seeds and put pellets in. Hand fed him a few of them and he was hooked. Pretending to eat the pellet and then giving it to them is a good method usually. And for getting him to eat veggies if he's not a veggie fanatic you can put your veggies with a little bit of his favorite fruits in the food processor. This will make them more appetizing to him. You can freeze the extras in little ice cube trays. Just pop out some of the fruit/veggie mix each day, thaw it (either leave it out or pop it in the microwave for 10 seconds) and voila!
That's just a quick diet overview. If you want more info I can give you more
I read online that all seed diets can increase the chance of tumor in birds and that a sign of tumor can be a swollen nare. So that could possibly be it? But they also said their poop and other things usually change when they have a tumor so maybe not. My grandma's canaries each have one swollen nare (its huge) and they're on an all seed diet. So maybe there's some kind of connection.
Hello everyone.. yesterday me and Elijah my Gcc went for a drive to my other house. When we arrived at the other house, I noticed that one of Elijah's nare's was bigger than the other. It looks swollen. I immediately brought him back home in hopes that he would settle down, however this moring it's still swollen. There is no discharge coming from the nares, no sneezing more than usual and overall he was acting normal last night, eating, drinking, & bobbing his head. I am a new conure mommy and I am really worried. I called a vet and he told me not to bring him right away, just to watch him and make sure everything remains normal and to come in for our appointmnet on saturday. I had to come to work today and there will be no one there to watch him. I will go at lunch and straight to him after work, but I am still extremely worried. can anyone offer any advice? 
