Are there ways to correct a barrel chest in a 22 year old?

Without photographs it's impossible to comment specifically. There are some very aggressive operations to correct chest wall abnormalities directly. Breast augmentation however can often times camouflage these substantially.

Unfortunately, without the photos-- it is impossible to give accurate assessment-- please upload the photos. Sometimes you can hide the barrel chest by high profile implants over the muscle with attention to maximizing the cleavage. 

It may be possible to hide a barrel chest by having breast implants to improve the relationship of your bust to your waist.  This really depends on your current breast size, your waist and how severe the barrel chest is.  It is good idea to see a plastic surgeon who can do 3D imaging and give you an idea of how breast implants may look if you had them placed and what size would give you a result that can make a difference. 

Difficult to give you  precise advice without viewing pictures or in-person examination; consider sending frontal/side view photographs with your next post. Sometimes, breast augmentation surgery is a good option to help “camouflage” chest wall aesthetic concerns.  You may find the attached link, demonstrating some example cases, helpful to you. Best wishes.

Thank you for your question.  Surgical procedures to alter your chest are major reconstructive  procedures that carry significant risk and will cause scarring.Breast augmentation could make your breasts more proportional to your chest with and help camouflage the barrel chest deformity.