There are a lot of terminology, and I am trying to be as understandable as I can be. English is my fourth language, so sometimes I have difficulties making my points :)
It's often the result of buying a jacket with a sleeve pitch that is the opposite of a person’s natural posture. That is–if you have the posture of a military soldier and buy a jacket that is designed for slightly slouched shoulders, then when you sit down, the fabric behind your neck may bunch up and stick out. To test out this phenomenon, pull your shoulders backwards and notice how excess fabric gathers on you back.
On the other side, if you have naturally sloped shoulders and buy a jacket made for a very upright posture, then the same back bunching phenomenon could occur when you sit down. To understand this result, slouch your shoulders forward, while pulling the fabric on your shoulder backwards.
As I said you have high shoulders, so you may need to shorten the collar and possibly lower it - this a tailor can do for you. But you can also find suits with different positions of armholes and different shoulders (Soft, much padded etc) - It also depends a lot on fabric.
Have you tried suits by the Hugo label? They are often a bit more fashion forward, thus more slim silhuette, higher armholes etc.
If I were you, I'd take any time in the world to try different styles... It's difficult for me to judge your body type on these photos, but different tailor styles works for different builds. I personally really love the italian styling. I personally have big shoulders, so I really like the neopolitan tailoring house style, where usually there's no extra height or breadth to the shoulder, making them appear smaller and rounded. This way, it doesnt add more to my shoulders than what I already have. These also have a much more casual expression tbh ;)
The armani suit you tried on is too big for you. I always tell my customers, that I follow the rules of "As loose as necessary, as tight as possible".
Hugo (red label Hugo Boss) have higher armholes, Burberry have some wonderful suits aswell with the same style. I also believe the "Brook Brothers" Milano cut have it! Go to stores and try them out, do whatever to gain information of your salespeople. Some of them are very knowledgable, and some of them have absolutely no clue!
Edit: Btw, there are many people on this board, with a lot more knowledge than me, and also experience (wearing suits, getting suits bespoked, and selling/creating suits professionally) but I am very passionate about suits, and I really try to do this to help out with what I can do, until I simply don't have enough expertise :)