Don't let it get to your head. Success, I mean. I didnt say you shouldn't take pride in your achievements. You should. You could even talk about it. But don't take it to heart. If you let your achievements define you, then what will your failures speak of you? You are simply much more than what you have achieved (or failed at).
As you climb up the ladder and start to manage people, you will start to taste 'power'. things you use to do yourself, you now get to 'delegate'. you push one button, and things get done (or are supposed to get done). it's easy to start feeling high and mighty. Don't. You are just doing your job like every one else. It's not who you are.
There should be nothing that your direct reports (i hate the word 'subordinates') do that you wouldn't do yourself. Think about that. You should be able and willing to do whatever they do, even if you are boss. Standing in line and waiting for your turn. Picking up litter. Cleaning up after you are done with your meal. Carrying your own stuff. Nothing should remain too 'small' or too 'low' for you to do.
And this will earn you their respect. And you become even more effective as a manager.
It is ultimately so liberating to not be so beholden to your position, your title. I am reminded of this when i travel. Out there, I commute, I do dishes, I fix my own bed (which I still do even here). I am ordinary person. Because I really am.
We all are. And that's what makes everything great. All small, ordinary people working together to do great things.