tteugeoun eumsigeul meogeoseo ibi apayo.

Here it means hot in temperature.

• 뜨거운 음식 = hot food
• 매운 음식 = spicy food

This is an important distinction, because English hot food can mean either one, but Korean usually separates them clearly.

The dictionary form is 뜨겁다.

When this kind of word modifies a noun, it uses a noun-modifying ending, often taught as -(으)ㄴ. But 뜨겁다 is a ㅂ-irregular word, so the ㅂ changes to 우 before vowel-initial endings.

So:

• 뜨겁다
  • -은
• becomes 뜨거운

That is why you get:

• 뜨거운 음식 = hot food

So 뜨거운 is just the correct modified form of 뜨겁다.

Because 음식 is the object of 먹다 (to eat).

• 음식 = food
• 음식을 = food + object marker

Since 음식 ends in a consonant, it takes -을 rather than -를.

So:

• 음식을 먹다 = to eat food

먹어서 is from 먹다 + -어서.

In this sentence, -아서/어서 shows a reason/cause:

• 뜨거운 음식을 먹어서 입이 아파요
• My mouth hurts because I ate hot food

This ending can sometimes also sound like after doing X, but here the most natural meaning is because or so.

A natural English sense is:

• I ate hot food, so my mouth hurts.
• My mouth hurts because I ate hot food.

Because in Korean, the thing that hurts is usually treated as the subject, not the object.

So:

• 입이 아파요 = the mouth hurts

This is very common with body parts and feelings/states:

• 머리가 아파요 = My head hurts / I have a headache
• 배가 아파요 = My stomach hurts
• 눈이 아파요 = My eyes hurt

English often says my mouth hurts, but Korean structures it more like the mouth is painful.

Korean often leaves out my, your, his, etc. when the owner is obvious from context.

So 입이 아파요 naturally means:

• My mouth hurts
  if the speaker is talking about themself

You do not need to say 제 입이 아파요 unless you want to be especially clear or contrast it with someone else’s mouth.

This is very normal in Korean, especially with body parts.

Usually 입 means mouth.

In this sentence, 입이 아파요 most naturally means that your mouth hurts, probably because the hot food burned it.

If you specifically mean lips, Korean usually says:

• 입술 = lips

So:

• 입이 아파요 = my mouth hurts
• 입술이 아파요 = my lips hurt

The dictionary form is 아프다.

When -아/어요 is added to a ㅡ-stem verb or adjective, the ㅡ usually drops.

So:

• 아프다
  • -어요
• becomes 아파요

This is a very common pattern:

• 바쁘다 -> 바빠요
• 슬프다 -> 슬퍼요
• 아프다 -> 아파요

So 아파요 is the normal polite present form.

이/가 and 은/는 have different jobs.

Here, 입이 아파요 is the neutral, natural way to say my mouth hurts. It simply marks mouth as the thing that hurts.

If you say 입은 아파요, it sounds more like:

• As for my mouth, it hurts
• or My mouth hurts, though...

That can feel contrastive, as if you are comparing it with something else.

So in a plain statement, 입이 아파요 is the better choice.

It is in the standard polite -아요/어요 style.

That means it is appropriate for everyday conversation in many situations:

• talking to strangers
• talking to coworkers
• talking to teachers
• talking politely in general

The sentence is polite, but not formal.

A more formal version could be:

• 뜨거운 음식을 먹어서 입이 아픕니다.

A natural pronunciation is approximately:

뜨거운 음식을 먹어서 입이 아파요
-> 뜨거운 음시글 머거서 이비 아파요

A few sound changes to notice:

• 음식을 sounds like 음시글 because the final consonant links to the next syllable
• 먹어서 often sounds like 머거서
• 입이 sounds like 이비

So even if the spelling looks one way, connected speech can sound a little different.