Yes, and OP, just in case this wasn't clear, when I said it was important to spend time with family and friends, I was lumping significant others into that category. It's important to spend time on your core relationships, especially partnerships.
There's nothing wrong with competing with yourself or others, as long as you don't take it too seriously and it promotes social harmony. Playfulness (which is separable from competitiveness) can be an intrinsically joyful way of experiencing everyday social interactions and tasks, and that's the way of being that I was advocating in my previous post.
Another concern I noticed in your first post is that you sound like you might be very extrinsically motivated by approval from others and recognition. Generally speaking, extrinsic motivations tend to be flimsy and ultimately unfulfilling reasons to do something. To make the sacrifices that medicine entails, we need intrinsic motivation, a complex set of experiences, feelings, goals and values that sustains us to keep going even when it's hard, even when no one knows or cares what we're doing--or even worse, when people whose opinions we care about actually do know about it and disapprove of and doubt you because you look like an unrealistic, foolish perfectionist, or because you're doing something that's not in your self interest because there's something you care about more than yourself.
What would you fight for and what would sustain you even in the absence of any external gratification, or even in the presence of active doubt and disapproval from others (which it sounds like you might not enjoy the feeling of)? The approval that comes with getting into a fancy MD school, a larger paycheck, prestige? Or the desire to form therapeutic relationships with patients and to help them feel and function better as much as you can?
On that note, you also need to take care to not act like a perfectionist. It's important to know how to prioritize based on your values and what you care about at the end of the day when no one is watching. However, it's also also important to know when to fold, to say "good enough", to surrender, especially when it comes to writing those papers you mentioned, for instance. It's also important to know how and when to split larger long-term projects into smaller, relatively manageable chunks. Like it says in the Scrubs theme song: "I'm no superman".