У дочки была маленькая сыпь на шее, но к вечеру она прошла.

Russian often uses у + genitive to express that someone has something or that something is with / on / affecting someone.

So:

У дочки была маленькая сыпь
literally means something like At the daughter there was a small rash,
but in natural English it means The daughter had a small rash.

This is a very common Russian pattern:

• У меня есть брат = I have a brother
• У ребёнка температура = The child has a fever
• У дочки была сыпь = The daughter had a rash

So the possessor is not the grammatical subject here.

Because у requires the genitive case, and дочка in the genitive singular becomes дочки.

Basic pattern:

• nominative: дочка
• genitive: дочки

So:

• дочка = daughter
• у дочки = of the daughter / with the daughter / the daughter has

Дочь is the basic word for daughter.
Дочка is a very common affectionate or more everyday form.

So:

• дочь = daughter
• дочка = daughter, daughter dear, little daughter

In many real-life contexts, Russian speakers naturally say дочка when talking about their own daughter. It does not always mean the daughter is very small; it often just sounds warmer and more personal.

Была is the past tense feminine singular form of быть.

It agrees with сыпь, not with дочки.

That is an important point:

• у дочки = possessor, in the genitive
• сыпь = the thing that existed, so it functions as the grammatical subject

Since сыпь is feminine singular, the verb is also feminine singular:

• сыпь была
• not сыпь был
• not сыпь было

Both words are in the nominative singular feminine:

• маленькая = feminine singular nominative
• сыпь = feminine singular nominative

They match because adjectives agree with the nouns they describe in gender, number, and case.

So:

• маленькая девочка
• маленькая проблема
• маленькая сыпь

Here маленькая сыпь means a small / slight / mild rash.

Because на is used here to mean on in the sense of location, and with location на normally takes the prepositional case.

So:

• nominative: шея = neck
• prepositional: на шее = on the neck

This is the normal pattern:

• на столе = on the table
• на руке = on the arm/hand
• на шее = on the neck

К вечеру means by evening or toward evening.

The preposition к takes the dative case, so:

• nominative: вечер
• dative: вечеру

This expression often means that something changed or was completed by that time:

• К утру стало лучше = By morning it got better
• К вечеру дождь закончился = By evening the rain had stopped
• К вечеру она прошла = By evening it had gone away

So к вечеру gives the time point by which the rash disappeared.

Here прошла comes from пройти, and with things like symptoms, pain, swelling, rash, fever, etc., it often means to pass, to go away, or to clear up.

Examples:

• Боль прошла = The pain went away
• Температура прошла = The fever passed
• Сыпь прошла = The rash went away / cleared up

The form прошла is feminine singular because it agrees with сыпь, which is feminine.

It refers to сыпь.

Grammatically, both дочка and сыпь are feminine nouns, so at first glance она could seem ambiguous. But the meaning of the sentence makes it clear:

• the daughter went away by evening does not make sense here
• the rash went away by evening does

So Russian relies on context here, just as English often does.

Because прошла is perfective, and it presents the rash as having fully gone away — a completed result.

That fits the sentence well:

By evening, it had gone away.

If you used проходила, that would be imperfective and would suggest an ongoing process, repetition, or a different kind of context. In this sentence, the speaker is talking about the finished outcome, so прошла is the natural choice.

The word order is quite natural and neutral:

У дочки была маленькая сыпь на шее, но к вечеру она прошла.

Russian word order is flexible, but different orders shift emphasis.

For example:

• У дочки была маленькая сыпь на шее = neutral
• На шее у дочки была маленькая сыпь = more emphasis on where it was
• Маленькая сыпь у дочки была на шее = possible, but more marked

The second clause is also natural:

• но к вечеру она прошла = but by evening it went away

Putting к вечеру early helps frame the timing before the result.

Russian has no articles like a or the.

So дочки, сыпь, шее do not need extra words for definiteness or indefiniteness. The listener understands from context whether something is a rash, the rash, a neck, the neck, and so on.

In this sentence:

• маленькая сыпь is understood as a small rash
• на шее is understood as on her neck / on the neck, depending on context

Russian usually lets context do that job.

Literally it is small rash, but in natural usage it often means something like slight, minor, or mild.

With medical or bodily symptoms, Russian sometimes uses size words in a way that overlaps with severity or extent.

So маленькая сыпь can suggest:

• the rash covered only a small area
• the rash was not severe
• the rash was minor

The exact nuance depends on context.