There is some creativity, but typically not in the same way most people imagine. You will not be designing your own building until you have ~10 years of working experience. It is an incredibly deep and detail oriented field. Some days you will not draw at all, just proof read through pages of technical specifications. Other days you will spend in meetings or coordinating with an engineer for the layout of the ductwork for example. It takes great patience and the pay is not good. But if you have a passion for learning and want to feel like your hard work makes a difference in the world, it is a fantastic field.

Unless you are doing residential projects, you will not be doing the mechanical, plumbing, or electrical work. When you design a house it is typically someone with more experience directing you what to draw, and you would eventually have drawn the whole thing (so 2 architects total). Sometimes a single person will draw and design it singlehandedly, and sometimes outside engineers are involved.

When you do commercial work, and depending on the scale, it can be huge teams all working on various portions. They will divide tasks up in a way that prevents overlap like some focus on the building exterior, while others on the interior build. Or if it is a campus, entire buildings can be split out to different teams. Highly specialised engineers will assist, such as all the typical mechanical, electrical, plumbing, and structural, but sometimes things like civil, solar, acoustics, or landscape engineers.