sSomeone iIn mMy hHead

This is a topic sentence, so all the first letters of the words (except articles like a/an) are to be written in the capital letter.

What should I do if I have a silly, private thought that I want to share?

Let me share something that's on my mind.

In short, I think I have a crush on someone that I've never met in person...

It's a once-in-a-blue-moon thing for me.

Or:
This kind of thing never happens to me.

This has never happened to me before.

I've never felt this way before.

I've never developed a crush in this way before.

sSomeone Is in mMy hHead / Someone Is on My Mind

Let me share something that’s on my mind.

What should I do if I have a silly, private thought that I want to share?

It would make more sense to have the “I” here be “you.” Since this question feels related to the next question. Ie “what do you do if… Do you have anyone…”

Once you’ve posed these questions to the reader, you then can introduce that you do not have anyone.

Do you have anyone nearby that you can (have a) chat with?

It's / this idea has / this thought has been stuck in my head and makes it hard to focus on anything.

The “it” here is unclear what it refers back to. Especially if you change the “I” to “you” as recommended.

In short, I think I have a crush thaton someone who I've never met in person...

Generally refer to people with “who/whom” depending on the context. “That” or “which” is for things or animals.

It's a once-in-a-blue-moon feeling / opportunity / romance for me.

“Once-in-a-blue-moon” is a compound adjective, so you need a noun for it to modify.