Exactly what SunnyClover said...A lot of their "yelling" or "screaming" has to do with the fact that they are "Flock" Animals, and even if you're not paying direct attention to your bird, she still has an innate need to be "among her flock" like they are naturally. So making sure that #1) Her main-cage is located in the room of your home where you and others who live there spend most of their time when you/they are home, usually the living room, family room, etc., just doing this can help tremendously. Just being in the same room as you when you're home will make her feel comforted, secure, and much less stressed/anxious..So when you're watching TV, reading, eating meals, talking, having visitors over, playing games, etc., just having her cage located in that room (if it's not already) will not only stop the screaming (which starts out typically as "contact calling" you and then turns into screaming), but it will also encourage her to entertain herself inside of her cage...So if her cage is located in a spare bedroom or room other than the "main room" of your home, that's the first thing you need to do, relocate it to the main-room where people spend the most time, so she will no longer be hearing you/knowing that you're home but not able to see you/be with her "flock"...
And if her main-cage is already located in the "main room" of your home, then the other thing you can do is to buy/build a portable T-Stand/Play-Stand for her that you can move from room to room with you...Then whenever you go into another room away from her main cage, say you go into your office to get on the computer, you're cooking/eating in the kitchen, you're family is eating their meals in the dining room or wherever you eat meals (this is a big one, they want to eat with their flocks), if you go to another room to watch TV or do whatever, simply move the portable T-Stand/Play-Stand to the room you're going to and just take her into that room, put her on her stand, and then do what you do...It doesn't mean that you have to be paying her attention 24/7 whenever you're home, but parrots are flock-animals and they naturally desire/need to be among their flocks, and when they know their flock-mates are there but not with them or within their sight, this is the result...So just put her in the room on her portable T-Stand/Play-Stand and make sure she has a toy to chew on/play with attached to the stand, and she'll most-likely happily entertain herself without any screaming/contact-calling because she can see you...So you don't have to have her constantly on you or be interacting with her, but whenever you or another "flockmate" is in the home, just letting her be in the same room with you/within her sight will help tremendously with this issue"[B/]. Just keep reminding yourself that she's a "Flock" animal, and that her contact-calling/screaming to be with you when she knows you are at home is completely normal for her...
****NEVER yell at her, scold her, tap her on the beak, etc. Parrots are not at all like dogs or cats, they do NOT respond to negative-reinforcement at all...Your Sun Conure has the intelligence of a 3-4 year-old human child, she can understand logic and use reasoning...And if you "scold" her, yell at her, raise your voice in an aggressive/angry way, tap her on the beak or "spank" her in any way, the result you're going to end up with is going to be a bird who no longer trusts you and will not allow you to touch her any longer...You always want to use "Positive Reinforcement" when you're trying to teach your bird to do something or not do something, their favorite treat is usually the best way to do this (ONLY give her very favorite treat to her when you are teaching/training her, no other time, because it needs to be something that is extra-special to her and that she desires because she doesn't get it very often)...
Good luck!
