We usually say, "He was called up." As that implies military service we don't usually add 'to the army.' Example: In wartime many people are called up. If you want to specify which service you could say, "He was called up in 1939 and chose to serve in the navy." So, in your writing, you could say, "I was called up." "I served for several years." "After serving in the army..." or "After my army service.... " There is one other possibility I should check,,, when you say "He was called to the army... " do you mean the government ordered him to go, or do you mean he had the urge to join? (Do you mean he WANTED to join and had a feeling he must do it?) I don't think you mean that he chose to go... but sometimes people say they felt 'called.' They say, "The church was my calling. I was called by God." And you can say it about the army, "The army was his calling." "He felt called." This is why it is important to check the difference between 'called' and 'called up." (!)

Called up or conscripted.

In the US, if you are required to go into the army, you are "drafted into the army." If you chose to go, you "enlisted in the army." (We don't have compulsory service by everyone like some other countries.) Then: After serving in the army, I entered the institute, where I chose to study management. I earned my qualification as an automobile mechanic. I'm not sure "management" is the word you want here. We would use "I entered a technical program." for an automobile mechanic's program.