You are indeed thinking too hard about it. This is a classic case of performance anxiety and nothing more. If you can get hard and achieve orgasm by hand and by yourself but are having trouble in a partner situation, that's performance anxiety. I mean, when you think about it, it is a situation that's fraught with tension.

You're a healthy, able-bodied young man. Try and chill out and give yourself a lot more foreplay time in advance to achieve a nice, solid erection. Sounds like you're also rushing things. That's easy to do when you're new at that. Good luck!