Q:

Is every sentence we write or utter either true or false?

Please read the complete description before putting any answer / comment, Thank you.
I've been just thinking through this question which I can frame it like this:
Can I write or utter any sentence which is neither false nor true?
Ok, after I've seen couple of answers (Thanks for the contributions), I want to edit my question.
one of the answers I've got:

A question is neither true nor false.

Understand, that sentence can be described as interrogative, but let's follow this:
If I utter May I know your name? now, what I just uttered has come out of the truth hood which indicates that I don't know your name, so in this case, the sentence I uttered is a by product of the truth I have
Next thing I've got

self-referential sentences such as This sentence is false.

It reminds me a paradox (forgot its name), nonetheless, This sentence is false even though the truth value of your example is undetermined..it is true that your example is self-referential, which in-turn created with a true intention.
So far things have fallen under truth...
More edits:
There are couple of things I want to share, first is to address what  I mean by the word "sentence": a thing (in language) created using words to describe my thoughts (a brain activity) or sometimes use to describe my (r)eality that I am seeing or the reality that is accessible to me.
Secondly, I spent some more time to think through my question, the more I think, I've come to this conclusion. there is no bi-valance and there is no true or false, there is just only one thing and that one thing is the origin of everything that follows....And that thing is

The Truth.

Because think of this, even if I ever were to lie (lies formed out of falsity), In-order for a lie to be a lie, it is has to come from The Truth.

it is true that I am lying.
it is true that the lie I told doesn't bear the truth.
it is true that my intention is true enough to form a lie.
it is true that the falsity used in my lie is truly false.
it is true that a lie can't become true.
And it is true that the true premises never form a false conclusion

So I just see only one thing: The Truth and I wonder were you people seeing it?
To mention: A comment I put as a reply to one person has been silently deleted (been there for a day) and I think, it got to be pretty uncomfortable for whoever did it-- Remember, The Truth is on you, can't escape.
What I commented: "you need to read the description too before comment".

A:

Various candidates would be:
self-referential sentences such as
"This sentence is false."
opinion-based sentences such as
"Chocolate is the most delicious ice cream flavor."
sentences where the truth value depends on the referents:
"I am awake right now." (indexical) "The team went on to win the cup." (context)
sentences with metaphor / poetry / nonsense:
"Anger reflects the clouds."
some counterfactual sentences:
"If the match hadn't ended in a draw, the away team would have won."
See also Are all non self-referential statements true or false?

A:

The OP asks the following:

Can I write or utter any sentence which is neither false nor true?

Yes. An example would be Tomorrow I will rise at precisely 6 am. That sentence today is neither true nor false. However, I will know tomorrow, but by then I will have a different sentence, perhaps: Today I rose at 6:30. That sentence could be viewed as either true or false since it is in the immediate past.
The logic textbook forallx describes three kinds of sentences that grammatically count as sentences although they are neither true nor false: questions, imperatives and exclamations. (pages 4-5)
That text also goes into detail about the kind of sentences to which logicians are interested in assigning truth-values. This is a subset of all possible sentences. These are the ones that logically count: (page 4)

To be perfectly general, we can define an argument as a series of sentences. The sentences at the beginning of the series are premises. The final sentence in the series is the conclusion. If the premises are true and the argument is a good one, then you have a reason to accept the conclusion.
In logic, we are only interested in sentences that can figure as a premise or conclusion of an argument. So we will say that a sentence is something that can be true or false.

What counts in logic are arguments. Arguments are composed of sentences on which one can assign a truth-value.
The OP also asks about self-referential sentences. These are sentences that should logically count. One should be able to assign a truth-value to them and yet when we do we run into paradoxes. These paradoxes are important. They challenge how we deal with that subset of sentences to which we want to assign truth-values. We not only want to assign truth-values. We also want to consistently do so.

P. D. Magnus, Tim Button with additions by J. Robert Loftis remixed and revised by Aaron Thomas-Bolduc, Richard Zach, forallx Calgary Remix: An Introduction to Formal Logic, Fall 2019. http://forallx.openlogicproject.org/forallxyyc.pdf

A:

Is every sentence we write or utter either true or false?

NO. A sentence is "a textual unit consisting of one or more words that are grammatically linked. [... The] words [are] grouped meaningfully to express a statement, question, exclamation, request, command or suggestion.
A question is neither true nor false.

