Is the questioner considered to be unjust to his colleagues who are older and more senior than him because he was nominated for an overseas training course and assumed a supervisory position in the department, bearing in mind that these nominations came from the managers in appreciation of his competence, and were not by his own choosing?

For managers and officials, it is permissible to nominate those they deem worthy of courses, positions, and rewards. The presence of those with more seniority does not prevent this. Therefore, there is no sin in what you mentioned, nor is there any injustice in it. Strive in your work and perfect it, for the Prophet, peace and blessings be upon him, said: "Indeed, Allah loves that when one of you does a job, he perfects it."