Если после укуса болит рука, лучше показать её врачу.

Because после always takes the genitive in Russian.

• укус = bite
• после укуса = after a bite

So this is a standard preposition + case pattern:

• после урока = after the lesson
• после работы = after work
• после укуса = after a bite

Because рука is the subject of the verb болит, so it stays in the nominative.

Russian structures this idea as the arm hurts, not literally it hurts the arm.

So:

• болит рука = the arm/hand hurts
• болит голова = the head hurts
• болят зубы = the teeth hurt

In other words, the thing that feels pain is grammatically the subject in Russian.

Russian often leaves out possessive words like my, your, his, especially with body parts, when the meaning is obvious from context.

So Russian naturally says:

• болит рука = your arm hurts / the arm hurts rather than always saying:
• болит ваша рука

If you wanted to make the person explicit, you could say:

• Если после укуса у вас болит рука...

But in general advice, leaving it out sounds very natural.

It can mean either hand or arm, depending on context.

Russian рука covers the whole upper limb more broadly than English hand. If Russian needs to be more specific, it can use:

• кисть = hand, specifically the hand part
• рука = arm/hand in general

So in this sentence, English might translate it as either hand or arm, depending on what sounds more natural in context.

Here лучше means it is better or you’d better.

Russian often uses лучше + infinitive to give advice in an impersonal way:

• лучше подождать = it’s better to wait
• лучше спросить = it’s better to ask
• лучше показать её врачу = it’s better to show it to a doctor

There is no explicit subject like you in the Russian sentence, but it is understood.

Because показать is perfective, and here the sentence is talking about one complete action: showing the hand/arm to a doctor.

• показать = to show once, to present
• показывать = to be showing, to show repeatedly/habitually

Since the advice is about a single visit or a single act of showing it to a doctor, показать is the natural choice.

In this sentence, её means it, not her.

It refers back to рука, which is a feminine noun in Russian. Russian pronouns agree with the grammatical gender of the noun:

• рука = feminine
• её = her/it (accusative or genitive form, depending on context)

Here it is the direct object of показать, so:

• показать её = show it

English uses it for objects like arm/hand, but Russian uses the feminine pronoun because рука is feminine.

Because врачу is the indirect object: the person to whom you show something.

With показать, Russian often uses this pattern:

• показать что? = show what? → direct object
• показать кому? = show to whom? → dative

So:

• её = what is shown
• врачу = to the doctor

Compare:

• дать книгу другу = give the book to a friend
• показать снимок врачу = show the image to the doctor

Yes. Russian word order is fairly flexible.

This sentence starts with the if-clause, which is very natural:

• Если после укуса болит рука, лучше показать её врачу.

But you could also say:

• Лучше показать её врачу, если после укуса болит рука.

The meaning stays basically the same. The original version feels natural because it presents the condition first and then the advice.

Yes. The sentence is impersonal, but the understood meaning is something like:

• you should show it to a doctor
• it’s better to show it to a doctor
• one should show it to a doctor

Russian often gives advice this way without saying you explicitly. That makes the sentence sound general and natural, like a piece of practical advice rather than a direct command.