Haluan myös tarkistuttaa silmäni uudestaan, jos näöntarkastuksessa näkyy muutos.

Tarkistaa means to check something yourself.

Tarkistuttaa means to have something checked or to get something checked by someone else. It is a causative verb: the speaker wants a professional, such as an optician or doctor, to do the checking.

So in this sentence, tarkistuttaa is the natural choice because the speaker is not checking their own eyes personally.

After haluta (to want), Finnish normally uses another verb in the first infinitive.

So:

• haluan tarkistaa = I want to check
• haluan tarkistuttaa = I want to have something checked

This is the standard Finnish pattern for want + verb.

The ending -ni means my.

So silmäni means my eye or my eyes, depending on context.

Finnish often uses a possessive suffix instead of a separate word like my. So instead of always saying minun silmäni, Finnish can simply say silmäni.

This is something that often surprises English speakers.

With possessive suffixes, Finnish forms can sometimes look the same in singular and plural. So silmäni can mean either my eye or my eyes.

Context tells you which meaning is intended. In a sentence about an eye or vision check, it is very natural to understand silmäni as my eyes. If the speaker meant one specific eye, they would often make that clearer, for example:

• vasen silmäni = my left eye
• toinen silmäni = my other eye

Because Finnish can express possession with a suffix.

Here, -ni already means my, so silmäni is enough.

You can also say minun silmäni, but that is more explicit or emphatic. In many normal sentences, the suffix alone is the most natural option.

Finnish makes compound nouns as one word.

Näöntarkastuksessa breaks down like this:

• näön = of vision / of sight
• tarkastus = inspection, check, examination
• -ssa = in, inside, during

So näöntarkastus means eye test / vision exam, and näöntarkastuksessa means in the eye test or during the eye test.

Writing it as one word is completely normal Finnish compound formation.

It is in the inessive case, marked by -ssa / -ssä.

The inessive often means in or during. So here:

• näöntarkastuksessa = in the eye test / during the eye test

In this sentence, during the eye test is probably the most natural way to understand it.

Näkyä literally means to be visible, to be seen, or to show up.

In this sentence, it does not focus on a person doing the seeing. Instead, it means that a change shows up, appears, or is visible in the examination.

So jos näöntarkastuksessa näkyy muutos is literally something like:

if a change shows up in the eye exam

That is why English often translates it more naturally as if the eye test shows a change.

Because muutos is the subject of näkyy.

The structure is basically:

• muutos näkyy = a change shows up / a change is visible

Since muutos is the thing that appears, it stays in the nominative basic form.

Finnish often uses the present tense for future meaning when the context makes the time clear.

So:

• jos ... näkyy muutos can mean if a change shows up
• and in context also if a change will show up

Finnish does not normally have a separate future tense like English does.

Yes, but the nuance changes.

• jos näkyy muutos = if a change shows up
  This is a normal, straightforward condition.

• jos näkyisi muutos = if a change were to show up
  This sounds a bit more tentative, hypothetical, or less direct.

In an ordinary statement about a real possibility, näkyy is the more natural choice.

Both mean again or anew, and both could work here.

Very roughly:

• uudestaan = very common in everyday language
• uudelleen = sometimes a bit more formal or written in tone

In this sentence, uudestaan simply means again: the speaker wants to have their eyes checked again.

Finnish word order is flexible, and words like myös are often placed near the thing they modify.

Here, Haluan myös tarkistuttaa silmäni uudestaan means:

I also want to have my eyes checked again

So myös adds also to the wanting/action.

If you wanted to emphasize I too, Finnish would more often use -kin, for example:

• Minäkin haluan... = I want to as well / I also want to

Because jos näkyy muutos is a subordinate clause.

In standard Finnish punctuation, when the main clause comes first and the subordinate clause follows, a comma is normally used before the subordinate clause.

So:

• Haluan myös tarkistuttaa silmäni uudestaan, jos ...

is standard punctuation.