kahun ga ooi hi ha, hana no tyousi ga waruku narukoto ga arimasu.

In 花粉が多い日, the phrase 花粉が多い means days when there is a lot of pollen.

Here, 多い is an i-adjective meaning many / a lot, and the thing that is many is marked by が:

• 花粉が多い = there is a lot of pollen

Then that whole phrase modifies 日:

• 花粉が多い日 = a day when there is a lot of pollen

So が is marking what is abundant.

In Japanese, descriptive clauses come before the noun they describe.

So:

• 花粉が多い日 literally = pollen-is-many day
• natural English = a day when pollen levels are high / a day with a lot of pollen

This is very common in Japanese:

• 雨が降る日 = a day when it rains
• 忙しい人 = a busy person
• 日本で買った本 = a book I bought in Japan

The は marks 花粉が多い日 as the topic:

• 花粉が多い日は、... = As for days with a lot of pollen, ... / On days when pollen is high, ...

It sets the context for what follows.

So the sentence structure is roughly:

• On days with lots of pollen,
  my nose condition sometimes gets worse.

調子 means condition, state, or how something is doing.

So:

• 鼻 = nose
• 鼻の調子 = the condition of one's nose

Using 鼻の調子 sounds more natural for talking about symptoms, how well your nose is functioning, congestion, irritation, and so on.

Compare:

• 鼻が悪い can sound odd or vague in many contexts
• 鼻の調子が悪い clearly means my nose is not doing well / my nose feels bad

調子が悪い literally means to be in bad condition.

It is used for many things:

• people feeling off
• body parts not functioning well
• machines not working properly

Here:

• 鼻の調子が悪い = my nose feels bad / my nose is acting up / my nasal condition is poor

In the context of pollen, it suggests symptoms like congestion, irritation, sneezing, or a runny nose.

Because なる often combines with the adverbial form of an i-adjective to mean become ....

For i-adjectives:

• remove the final い
• add く

So:

• 悪い → 悪く
• 鼻の調子が悪くなる = one's nose condition becomes bad

Other examples:

• 寒い → 寒くなる = become cold
• 高い → 高くなる = become expensive / higher

〜ことがある means there are times when ... or sometimes ... happens.

So:

• 悪くなることがあります = it sometimes gets worse / there are times when it gets worse

This makes the statement less absolute than 悪くなります:

• 悪くなります = it gets worse / it will get worse
• 悪くなることがあります = it may get worse sometimes

This is a very common pattern for talking about occasional events.

The structure is:

• dictionary form verb: なる
• nominalizer: こと
• existence verb: ある
• polite form: あります

So literally:

• 悪くなることがあります
• There are occasions of becoming worse

Natural English:

• it sometimes gets worse
• there are times when it gets worse

こと turns the verb phrase into a noun-like expression, which allows ある to say that such occasions exist.

They are doing different jobs in different parts of the sentence.

1. 花粉が多い日

   • が marks what is abundant: pollen

2. 鼻の調子が悪くなることがあります

   • が marks the subject of 悪くなる: the condition of the nose

So the sentence has two different clauses, and each clause can have its own が.

Yes, the meaning would be similar, but the phrasing would change.

• 花粉が多い日 = days with lots of pollen
• 花粉がたくさんある日 = days when there is a lot of pollen

Both are understandable.
However, 花粉が多い日 is more compact and very natural.

Not exactly.

• 鼻の調子が悪くなる focuses on the condition of the nose becoming poor
• 鼻が悪くなる is less natural in this context and can sound vague

When talking about allergies or temporary symptoms, 鼻の調子が悪い / 悪くなる is more idiomatic.

Here it is general.

• 花粉が多い日は、... means on days when pollen is high, ...

It is not talking about one specific day unless the surrounding context makes that clear. This kind of X日は、Y structure often means whenever X-type days occur, Y tends to happen.

Japanese often omits subjects when they are understood from context.

In this sentence, the listener can infer that 鼻の調子 refers to the speaker's nose, or to the relevant person's nose from context.

So Japanese does not need to say:

• 私は花粉が多い日は、鼻の調子が悪くなることがあります。

That would be possible, but often unnecessary.

Yes. It is polite because it ends with あります, the polite form of ある.

The sentence mixes plain forms inside the clause with a polite ending, which is completely normal in Japanese:

• 多い
• 悪くなる
• あります

This is a standard polite sentence style.

Yes. It strongly suggests a recurring tendency.

Because of:

• 花粉が多い日 = on days with lots of pollen
• 〜ことがあります = sometimes happens

the overall meaning is:

• When pollen is high, my nose sometimes acts up.

So it sounds like a general pattern, not a single incident.