Learn English – Another expression for “I remember”

I have no room for other things in my mind.
I have no space for other things.

Both of these are figurative speech, and they are acceptable as is. One might add the word extra or spare as well:

There's no spare room for anything else in my mind.
I have no extra space for new things in my brain right now.

(I decide to change the way you said other things, because it's hard to figure out what "things" are in your mind already, and what other things you don't have any room for.)

But, yes, you can use words like space when talking about the brain for the mind. In fact, the word attic is sometimes used to refer to the mind metaphorically, because it's in the upper part of our body, and it's used to store things. Doyle used this analogy in 1887, in a Sherlock Holmes story:

“I consider that a man's brain originally is like a little empty attic, and you have to stock it with such furniture as you choose.” (Sherlock Holmes, A Study in Scarlet)

As you guessed, words like space and room can also be used for a schedule, as well as a brain:

I'm sorry, I'm too busy; I don't have room to meet this week. Can we try for next week? I have more free space on my calendar then.

In addition to brains and calendars, you could also use such words to describe, say, a person's frustration level. For example:

My car won't start! Dammit! I don't have room for this right now.

might mean that the speaker is under a lot of stress, and this isn't a good time for his car to break down. Here's another example from a book:

As much as I don't have room for this in my life right now, I can't help but be intrigued. “What kind of plan?” I ask. (N.L. Shepherd, Stealing Bases)

One way to say this is to use the word skill, or the expression more skilled, much like you did in your question:

Jeff always beats me in golf. He is far more skilled than I am.

Playing checkers with my 9-year-old can be boring. She just doesn't have enough skill yet to play competitively yet.

The Oakdale high school team couldn't compete against the Olympic volleyball team; the skill level of their opponents would simply be way too high.

Macmillan defines the word skill as:

the ability to do something well, usually as a result of experience and training

You can also convey this sentiment with the expression can't compete:

I couldn't compete against against Brianna Stewart. She's about 6 inches taller than I am, and one of the best athletes in college sports.

My son tries to play chess with me, but he just can't compete.

We could play darts for money if you wanted to, but, I'm telling you, you won't be able to compete. I used to play in weekly tournaments for about ten years.

We finally had to close down our burger restaurant. We just couldn't compete against the McDonald's across the street.

When compete is negated in the sentence, it often implies a gross mismatch like the one you describe in your question.