Minha prima me deu carona porque o engarrafamento estava pior do que ontem.

Because minha has to agree with prima, the noun being possessed.

• prima = female cousin
• primo = male cousin
• minha goes with feminine singular nouns
• meu goes with masculine singular nouns

So:

• minha prima = my female cousin
• meu primo = my male cousin

The possessive agrees with the thing/person owned, not with the speaker.

Dar carona is a very common Brazilian Portuguese expression meaning to give someone a ride.

So:

• Minha prima me deu carona = My cousin gave me a ride

Literally, dar means to give, but dar carona works as a fixed expression.

Related expressions:

• dar carona para alguém = to give someone a ride
• pegar carona = to catch/get a ride

Example:

• Ela me deu carona até a escola. = She gave me a ride to school.

Me is the indirect object pronoun here, meaning to me.

So me deu carona literally works like gave a ride to me.

In Brazilian Portuguese, object pronouns often come before the verb in normal speech:

• Ela me ajudou. = She helped me.
• Ele me ligou. = He called me.
• Minha prima me deu carona. = My cousin gave me a ride.

This is called proclisis. In European Portuguese, pronoun placement can be different more often, but in Brazil, me deu is the natural everyday form.

This is a very important Portuguese pattern.

• deu is the preterite of dar
• estava is the imperfect of estar

They are used differently:

deu

The preterite is used for a completed event:

• Minha prima me deu carona = My cousin gave me a ride
  This happened once and is seen as finished.

estava

The imperfect is used for background, ongoing conditions, or descriptions in the past:

• o engarrafamento estava pior = the traffic jam was worse
  This describes the situation at that time.

So the sentence has:

• a main completed action: she gave me a ride
• a background situation: the traffic was worse than yesterday

This combination is extremely common in Portuguese.

Because here it means because, introducing a reason.

• porque = because

So:

• ...porque o engarrafamento estava pior... = ...because the traffic jam was worse...

Portuguese has several similar-looking forms:

• porque = because
• por que = why / for which
• por quê = why? at the end of a question
• porquê = the reason

In this sentence, the correct one is porque because it gives the cause.

Portuguese uses definite articles much more often than English does.

Here, o engarrafamento means the traffic jam or more naturally just traffic/the traffic situation in context.

Using the article is normal:

• o carro = the car
• a escola = the school
• o engarrafamento = the traffic jam

Even when English might say just traffic, Portuguese often prefers a structure with an article and noun.

Also, engarrafamento is a masculine noun, so it takes o.

Not exactly.

engarrafamento

This means a traffic jam, a backup, or heavy congestion.

trânsito

This means traffic more generally, as a system or the flow of vehicles.

So:

• O trânsito está ruim. = Traffic is bad.
• Há um engarrafamento enorme. = There is a huge traffic jam.

In your sentence, engarrafamento emphasizes that the congestion itself was bad enough to matter.

This is the comparative structure worse than yesterday.

• pior = worse
• do que = than
• ontem = yesterday

So:

• pior do que ontem = worse than yesterday

A few useful comparisons:

• melhor do que = better than
• pior do que = worse than
• maior do que = bigger than
• menor do que = smaller than

Example:

• Hoje está melhor do que ontem. = Today is better than yesterday.

Because pior is the normal comparative form of ruim.

Just like in English:

• bad → worse not usually more bad

In Portuguese:

• ruim → pior not usually mais ruim

So the standard form is:

• O engarrafamento estava pior.

You may occasionally hear mais ruim in some contexts or varieties, but for learners, pior is the form you should use.

In comparisons, do que means than.

• pior do que ontem = worse than yesterday

In many cases, especially in spoken Brazilian Portuguese, people may shorten this and say just que:

• pior que ontem

That is very common in speech and informal writing.

Still, do que is very clear and often taught as the standard full form, so it is a good form to learn.

Because ontem is an adverb meaning yesterday.

Time adverbs often appear alone:

• hoje = today
• ontem = yesterday
• amanhã = tomorrow

So:

• Hoje está quente. = Today it’s hot.
• Ontem choveu. = Yesterday it rained.

In the sentence, ontem is the reference point for the comparison:

• worse than yesterday

Yes. Brazilian Portuguese offers a few natural variations, depending on style and emphasis.

For example:

• Minha prima me deu uma carona porque o trânsito estava pior do que ontem.
• Minha prima me deu carona porque o trânsito estava pior que ontem.
• Como o engarrafamento estava pior do que ontem, minha prima me deu carona.

Notes:

• dar carona and dar uma carona are both common
• engarrafamento and trânsito are close, but not identical
• do que and que can both appear in comparisons

The original sentence is completely natural in Brazilian Portuguese.