Если после нового крема появилась сыпь, лучше сразу показать руку врачу.

Because после requires the genitive case.

• новый крем = nominative, new cream
• после нового крема = genitive, after the new cream

So both words change:

• новый → нового
• крем → крема

In this sentence, после нового крема means something like after using the new cream or after the new cream was applied. Russian often leaves that idea implied.

Because the subject is сыпь, and сыпь is:

• feminine
• singular

So the past-tense verb must agree with it:

• появился = masculine
• появилась = feminine
• появилось = neuter
• появились = plural

Even though сыпь comes after the verb, it is still the subject, so the verb agrees with сыпь.

It is nominative, because it is the subject of the clause.

The structure is:

• Если ... появилась сыпь = If a rash appeared

So сыпь is the thing that appeared.

A learner may be confused because the word comes after the verb, but Russian word order is flexible. The subject does not have to come first.

Both are possible, but появилась сыпь sounds natural when introducing new information: a rash appeared.

Russian often puts the verb first and the subject after it when presenting something that happened or appeared.

Compare:

• Сыпь появилась = more like The rash appeared
• Появилась сыпь = more like A rash appeared

The second version fits well when you are mentioning the rash as new information.

Russian often omits possessive words like my, your, his, etc. when the meaning is obvious from context.

So:

• показать руку врачу literally = to show the hand to a doctor
• but naturally it means to show your hand to a doctor

Since the person with the rash is clearly the one whose hand is meant, Russian does not need свою or вашу here.

You could say:

• показать свою руку врачу

but it is often unnecessary.

Because рука is the direct object of показать, so it takes the accusative case.

• nominative: рука
• accusative: руку

The verb pattern is:

• показать что? кому?
• to show what? to whom?

So here:

• руку = what is shown
• врачу = to whom it is shown

Because врач is in the dative case after показать.

With показать, Russian commonly uses:

• показать что кому
• to show something to someone

So:

• врач → врачу
• показать руку врачу = show the hand to a doctor

This is a very common Russian way to give advice.

• лучше here means it is better
• the infinitive показать tells what action is recommended

So the whole pattern means:

• лучше + infinitive = it’s better to ...

Examples:

• Лучше подождать. = It’s better to wait.
• Лучше сразу позвонить. = It’s better to call right away.

In your sentence, the subject is not stated because the advice is general and the person is understood from context.

Russian often leaves it out when it is obvious.

A fuller version could be:

• Если после нового крема появилась сыпь, вам лучше сразу показать руку врачу.

That means:

• If a rash appeared after the new cream, you should show your hand to a doctor right away.

But вам is often omitted when the sentence is giving general advice and the addressee is clear from context.

Because показать is perfective, and here the speaker means a single, definite action: go and show it to a doctor.

• показать = perfective, one completed act
• показывать = imperfective, repeated/process/habitual

So:

• лучше сразу показать руку врачу = it’s better to show your hand to a doctor right away
• показывать would sound more like repeated or ongoing showing, which does not fit as well here

Сразу means right away, immediately, or without delay.

It emphasizes that the action should be done promptly:

• лучше сразу показать руку врачу = it’s better to show your hand to a doctor right away

It often appears in advice, warnings, and instructions.

Yes, but the meaning changes slightly.

• лучше сразу показать руку врачу = it’s better to show your hand to a doctor right away
• нужно / надо сразу показать руку врачу = it is necessary / you need to show your hand to a doctor right away

So лучше sounds like advice or recommendation, while нужно and надо sound stronger and more necessary.

Because the sentence is about a condition that has already happened:

• Если ... появилась сыпь = If a rash has appeared / if a rash appeared

The idea is:

1. first, the rash appears
2. then, the advice applies

So the condition is already real or already observed, not something hypothetical in the future.

If you were talking about a possible future situation, you might say:

• Если после нового крема появится сыпь, ...
• If a rash appears after the new cream, ...

That would sound more like future-oriented advice.

Yes, it is natural, though it is a little compressed.

Russian often leaves out words like using, applying, or putting on when the meaning is obvious.

So:

• после нового крема can naturally mean after the new cream
• in context, that means after using/applying the new cream

A more explicit version could be:

• после использования нового крема
• после того как нанесли новый крем

But the shorter version is very common in everyday speech.

Yes, but the meaning is slightly different.

• показать руку врачу = show your hand to a doctor
• показаться врачу = see a doctor / go to a doctor to be examined

So показаться врачу is more general, while показать руку врачу specifically focuses on the hand.

Both can make sense depending on what you want to emphasize.

Because the sentence means to a doctor, not to doctors.

Russian often uses the singular for this kind of general recommendation:

• обратиться к врачу = consult a doctor
• показать руку врачу = show your hand to a doctor

It does not mean one specific doctor necessarily; it just means a medical professional in general.

Partly, yes.

The first clause is normal and personal:

• появилась сыпь = a rash appeared

But the second clause uses an impersonal recommendation structure:

• лучше сразу показать руку врачу = it’s better to show your hand to a doctor right away

There is no explicit grammatical subject like it or you, but the meaning is still clear. This is very common in Russian.