После падения медсестра туго обмотала лодыжку бинтом.

Because после requires the genitive case.

The dictionary form is падение meaning fall or falling.
Its genitive singular form is падения.

So:

• падение = nominative, dictionary form
• после падения = after the fall / after falling

This is a very common pattern in Russian:

• после урока = after the lesson
• после работы = after work
• после падения = after the fall

It can mean either, depending on context.

Russian often uses a noun where English might use either:

• a noun phrase: after the fall
• a gerund-like phrase: after falling

So падение can refer to:

• the event itself: a fall
• the act/process: falling

In this sentence, English would most naturally understand it as after the fall or after falling down.

Обмотала is the past tense, feminine singular form of обмотать.

That tells you several things at once:

• обмотать = to wrap around, to bandage by wrapping
• обмотала = wrapped
• the subject is female, because the past-tense ending is -ла

Since медсестра means nurse and is feminine here, the verb matches it:

• медсестра обмотала = the nurse wrapped

If the subject were masculine, it would be обмотал.
If plural, обмотали.

Обмотать is perfective, so обмотала presents the action as completed.

That fits the sentence well: the nurse finished wrapping the ankle.

So the sentence describes a completed event:

• После падения медсестра туго обмотала лодыжку бинтом.

If you used the imperfective обматывала, it would sound more like:

• she was in the process of wrapping it
• she wrapped it repeatedly
• or the sentence is focusing on the action itself rather than its completion

In a simple event sequence like after X, she wrapped Y, Russian usually prefers the perfective.

Because лодыжка is the direct object of the verb, so it goes into the accusative case.

Dictionary form:

• лодыжка = ankle

Accusative singular:

• лодыжку

So:

• обмотала лодыжку = wrapped the ankle

This is the normal pattern for a direct object after a verb like обмотать.

Because бинтом is in the instrumental case, which here shows the means or instrument used to do the action.

Dictionary form:

• бинт = bandage

Instrumental singular:

• бинтом

So:

• обмотать лодыжку бинтом = to wrap the ankle with a bandage

This is a very common Russian pattern:

• писать ручкой = write with a pen
• резать ножом = cut with a knife
• обмотать бинтом = wrap with a bandage

With this verb, Russian often uses the pattern:

• обмотать что чем
• wrap something with something

Here:

• что = лодыжку
• чем = бинтом

Туго means tightly.

It is an adverb, so it describes how the nurse wrapped the ankle:

• туго обмотала = wrapped tightly

It comes from the idea of something being tight or firmly drawn.
In this sentence, it tells you the bandage was applied snugly, not loosely.

Because that is a natural place for an adverb in Russian, but the word order is somewhat flexible.

Here:

• медсестра туго обмотала лодыжку бинтом

sounds neutral and natural.

You could also hear:

• медсестра обмотала лодыжку бинтом туго
• медсестра бинтом туго обмотала лодыжку

But those may shift emphasis slightly.

In this sentence, placing туго before обмотала straightforwardly highlights the manner of the action: she wrapped it tightly.

Because Russian has no articles.

So a noun like медсестра can mean:

• a nurse
• the nurse

and лодыжку can mean:

• an ankle
• the ankle

The exact meaning depends on context.

That is why one Russian sentence can correspond to several English versions, such as:

• After the fall, the nurse tightly wrapped the ankle with a bandage.
• After a fall, a nurse tightly wrapped an ankle with a bandage.

Usually the surrounding context tells you which is intended.

Russian often leaves possession unstated when it is obvious from context.

So лодыжку by itself can mean:

• the ankle
• his ankle
• her ankle
• the patient’s ankle

depending on the situation.

English often prefers an explicit possessive, but Russian does not always need one.

If Russian wanted to be specific, it could say things like:

• её лодыжку = her ankle
• его лодыжку = his ankle

But in many natural sentences, Russian simply uses the noun alone and lets context do the work.

Not completely. Russian word order is fairly flexible because the case endings show each word’s role.

This sentence has a neutral, natural order:

• После падения медсестра туго обмотала лодыжку бинтом.

That order presents the information smoothly:

1. time/background: После падения
2. subject: медсестра
3. manner + action: туго обмотала
4. object: лодыжку
5. instrument: бинтом

Other orders are possible, but they can change the emphasis. For example:

• После падения бинтом медсестра туго обмотала лодыжку
• Лодыжку медсестра после падения туго обмотала бинтом

These are grammatically possible, but less neutral.
So the original sentence is a good standard word order to learn from.