عندي دوار أيضا.

عندي literally means at me or with me. In Arabic, that structure is very often used to express have.

So عندي دوار is literally something like with me is dizziness, but in natural English it means I have dizziness or I feel dizzy.

Arabic also normally does not use a present-tense verb to be in simple sentences like this, so no extra verb is needed.

Usually, no.

The -ي in عندي already tells you that the speaker is I / me, so أنا is not necessary.
You can add it for emphasis:

أنا عندي دوار أيضًا = I have dizziness too

That sounds more emphatic, as if you are stressing I.

دوار means dizziness or vertigo.

In English, the most natural translation is often I feel dizzy, even though the Arabic structure is literally I have dizziness. In medical or symptom-list contexts, دوار is a very normal MSA word.

After عندي or لديّ, Arabic often uses an indefinite noun when saying someone has a symptom or condition:

• عندي صداع = I have a headache
• عندي حمى = I have a fever
• عندي دوار = I have dizziness

So دوار without ال is completely normal here. Using الدوار would sound more specific, as if you mean a particular known dizziness or the condition in a more definite sense.

أيضا means also or too.

So the sentence means I also have dizziness or I have dizziness too. It adds the idea that this is one symptom among others, or that the speaker shares this symptom as well.

Yes, it can move.

Putting أيضا at the end is very natural and often corresponds to English too:

عندي دوار أيضًا = I have dizziness too

You can also say:

عندي أيضًا دوار

That is also correct, and it can sound a bit more like I also have dizziness. The meaning is basically the same; the difference is mostly emphasis and style.

Yes.

لديّ دوار أيضًا is correct and means the same thing. Compared with عندي, لديّ often sounds a bit more formal or written.

So:

• عندي دوار أيضًا = very common and natural
• لديّ دوار أيضًا = also correct, slightly more formal

A common pronunciation is:

ʿindī duwār ayḍan

If you read it with full formal case endings, it can be:

ʿindī duwārun ayḍan

A few useful points:

• عندي = ʿindī
• دوار here is usually duwār
• أيضا = ayḍan

Here is the breakdown:

• عند = at / with
• -ي = me / my
• عندي = with me / I have
• دوار = dizziness
• أيضا = also / too

So the sentence is literally:

With me [is] dizziness also

But the natural English meaning is:

I also have dizziness / I feel dizzy too

This sentence is natural, especially when listing symptoms.

Another common MSA way is:

أشعر بالدوار أيضًا = I also feel dizzy

The difference is small:

• عندي دوار أيضًا focuses on having the symptom
• أشعر بالدوار أيضًا focuses on feeling dizzy

Both are correct.