For a tunic style shirt dress to fit properly through the shoulders and butt, it will often become quite baggy in the midsection, looking at best like a sack and at worst like lumpy sausage. This is because they are cut to fit loosely through the body, but the arm measurements do not increase proportionately. In a size that fits your arms comfortably, you are drowning in fabric everywhere else, and if you size down to create a cleaner line through the body, then your arms may feel squeezed which is especially uncomfortable during the hot and sticky summer months. Another issue is that tunic style dresses are generally very straight which leaves no room to accommodate any curves. The result is a tight fit through the shoulders and arms, billowing fabric through the upper body and then more tightness through the butt and upper thigh area. This highlights your widest part without taking advantage of the smallness of your waist, which is the opposite of the silhouette you should be aiming for.
You are probably wondering why I don't just suggest adding a belt around the waist to add some definition and easily solve the issue. This is a viable solution, but only if the dress is already a bit long. When you add the belt, you will lose length because fabric will have to be pulled in so far to reach your actual body. Depending on how a specific dress fits you, there is the possibility of losing a couple inches. The other downside is that the fabric will bunch around the waist, creating unwanted gathering that not only requires repeated adjustments, but will wrinkle the fabric.
When you are looking for a flattering shirt dress, I suggest looking for one that is designed with a belt in mind (although you should feel free to swap out the fabric belt they sell with the dress for a a skinny patent or metallic one) and that has a skirt that is slightly wider than the bodice. This will help reduce the extra fabric that is widening your midsection and give extra room to prevent unattractive pulling across your butt.