Esta camisa não me fica bem; preciso de outro tamanho.

Here ficar bem means to suit someone, to look good on someone, or to fit well in appearance.

So Esta camisa não me fica bem is not just about the shirt existing in a good state. It means the shirt does not look right on the speaker, or does not fit them well in the way it sits on the body.

With clothes, ficar bem often refers to appearance and fit together:

• Esse vestido fica-te bem. = That dress looks good on you.
• O casaco não me fica bem. = The coat doesn’t suit me / doesn’t fit me well.

Me means to me or on me here.

It shows who the shirt suits or fits well. A very literal way to think of it is:

• A camisa fica-me bem = The shirt sits well on me.

In the sentence:

• Esta camisa não me fica bem the me refers to the speaker.

This is very common with verbs that describe how something feels, looks, or fits to someone.

Because in European Portuguese, words like não usually force the pronoun to come before the verb. This is called proclisis.

So:

• fica-me bem = it suits me / it looks good on me
• não me fica bem = it does not suit me

After negation, me goes before the verb:

• Não me serve.
• Não me agrada.
• Não me fica bem.

This is especially important in European Portuguese. In an affirmative sentence, European Portuguese often prefers:

• Fica-me bem.

Because adjectives and determiners agree with the noun they describe.

• camisa is feminine singular, so you get esta
• tamanho is masculine singular, so you get outro

So:

• esta camisa
• outro tamanho

This agreement is one of the first things English speakers notice in Portuguese, since English does not change words this way.

Because precisar normally takes the preposition de in standard Portuguese, especially in European Portuguese.

So:

• preciso de ajuda = I need help
• preciso de dinheiro = I need money
• preciso de outro tamanho = I need another size

For a learner of Portuguese from Portugal, it is best to learn precisar de as the normal pattern.

Because outro often works by itself to mean another.

So:

• preciso de outro tamanho = I need another size

Adding um is possible in some contexts, but outro tamanho is the most natural choice here.

Compare:

• Quero outro. = I want another one.
• Preciso de outro tamanho. = I need another size.

For English speakers, this can feel unusual because English often uses another as a single word, while Portuguese uses outro without needing um in many cases.

They are similar, but not exactly the same.

• não me fica bem focuses on how it looks or how it fits on the body
• não me serve focuses more directly on size or whether it physically fits

So:

• Esta camisa não me fica bem = This shirt doesn’t suit me / doesn’t fit me well
• Esta camisa não me serve = This shirt doesn’t fit me

In your sentence, the second clause says preciso de outro tamanho, so size is clearly the problem. Because of that, não me serve would also make sense. But não me fica bem sounds a bit broader and more natural in many shopping situations.

Because bem is an adverb, and it goes with the verb phrase ficar bem.

You are not saying the shirt is good. You are saying it fits/looks good on someone.

So:

• A camisa é boa. = The shirt is good.
• A camisa fica bem. = The shirt looks good / fits well.

That is why bem is correct here, not boa.

Yes, it is natural and polite.

A speaker in Portugal could easily say:

• Esta camisa não me fica bem; preciso de outro tamanho.

It sounds like something you would say when trying on clothes and realizing the current size is not right.

Other natural alternatives include:

• Esta camisa não me serve; preciso de outro tamanho.
• Esta camisa está apertada/larga; preciso de outro tamanho.

Those alternatives are more specific:

• apertada = tight
• larga = loose

The semicolon links two closely related ideas:

• Esta camisa não me fica bem
• preciso de outro tamanho

It shows that the second idea is a direct consequence of the first.

You could also write:

• Esta camisa não me fica bem. Preciso de outro tamanho.

That would sound just as natural. The semicolon simply makes the connection a bit tighter in writing.

Yes. In European Portuguese, an affirmative version often uses the pronoun after the verb:

• Esta camisa fica-me bem. = This shirt suits me.

But with negation, the normal order is:

• Esta camisa não me fica bem.

So the sentence you have is already in the expected and natural order for European Portuguese.