The respiration system is compiled from various musculatures (among other structures, but we'll only focus on the involved muscles for the purposes of simplicity), including but not exclusive to the scalenes, SCM (sternocleidomastoid), subclavius, internal and external intercostals, rectus abdominis, transverse abdominis, internal and external obliques, psoas, quadratus lumborum, the pelvic floor, and of course, the diaphragm.
(photo from physio-pedia.com)
All of these muscles are important in the inspiration and expiration stages of breathing. Habitual breathing (not using focus or for sport) should include the concentric activation of the inspiration muscles (diaphragm, internal intercostals), and accessory muscles (pectoralis minors, SCMs, scalenes), and pelvic floor, along with the relaxation of the expiration muscles (external intercostals, transverse abdominals, rectus abdominis, internal/external obliques, quadratus lumborum, and psoas) during inhalation, and the opposite during exhalation. A chest breather will only use their upper structures to complete the breathing cycle, completely ignoring the use of their abdominal musculature, and overusing their neck muscles. Their diaphragm then gets "tight," and sometimes cramps or causes mid back pain. They will commonly have short breaths, dizziness, fatigue, frequent yawning, low energy, side stitches, and stiff neck/shoulders (especially a tight upper trap). They might even have numbness/tingling along their arms. Poor circulation and acid reflux are also common symptoms of chest breathers because of the overly tight diaphragm.
(photo from chronicbodypain.net)
The solution to overdoing it on top is to start doing on the bottom, right? Well, kind of.
I'm sure you've seen people who are really good at belly breathing. You might be one of those people. Your belly makes a nice rotund shape every time you inhale, perhaps from the belt line up to your ribcage. If you're "really good" at belly breathing, your dome belly will even reach to the top of your pubic symphysis, as it should. Go ahead, take a few of those really good belly breaths.
(image from buzzle.com)
Now notice what happens to your chest when you take those breaths. Any movement? No? Or it moves up and down (towards/away from your head)? Well, you're still not breathing properly. A proper inhalation should involve the chest wall and abdomen expanding outwardly equally, not one more than the other. By outwardly, I mean 360 degrees. You should have anterior, lateral, and posterior expansion.
Many people focus on actively belly breathing and "not being a chest breather," and as a result, they overdo it, and cause another dysfunction. It's kind of like if you sprained your left ankle, and instead of learning how to use the proper musculatures to even yourself out, you put all your weight your right foot, and end up with a compressed right hip. So what's the solution? Work on 360 breathing. Breathe with your chest, your abdomen, your sides, and your back. Put some Kinesio Tape or Rock Tape, or an elastic band around your abdomen, lower rib cage, and upper chest, and see if you can breathe into the bands, all at once. This is tricky to do all at once if you're not already accustomed to it, so you might want to just work on one aspect at one time, but remember to incorporate them all together, so as to not be dysfunctional in a different way.
(image from urbanwellnessstudio.ca)