Я забыла мочалку в ванной и пошла за ней уже в пижаме.

Because the speaker is feminine.

In the Russian past tense, verbs agree with the subject in gender and number:

• забыл / пошёл = masculine singular
• забыла / пошла = feminine singular
• забыло / пошло = neuter singular
• забыли / пошли = plural

So this sentence tells you that the speaker is a woman or girl.

In the past tense, Russian verbs do not show person clearly. They show gender and number, not I / you / he / she.

So забыла by itself could mean:

• I forgot
• she forgot

Context often makes it clear, and Russian can omit я, but using я makes the subject explicit.

Because мочалку is the accusative singular, used for the direct object of забыла.

The base form is:

• мочалка = washcloth / bath sponge / loofah

For many feminine nouns ending in -а, the accusative singular changes to -у:

• мочалка → мочалку

So:

• Я забыла мочалку = I forgot the washcloth

In this context, it most naturally means left it behind / forgot it there.

Russian забыть can work this way:

• Я забыл ключи дома = I left my keys at home / forgot my keys at home

So here the idea is not just that the speaker mentally forgot about the washcloth, but that she realized she had left it in the bathroom.

Two things are happening here.

1. Why в ванной?

After в, when you mean location and not movement, Russian usually uses the prepositional case.

• в ванной = in the bathroom

2. Why ванная?

Ванная is a very common shortened form of ванная комната = bathroom.

Originally ванная is an adjective, but in everyday Russian it often functions like a noun:

• ванная комната → ванная

That is why the form is:

• в ванной

Yes, but with verbs of motion, идти / пойти за + instrumental often means go get, go fetch, or go back for someone or something.

So:

• пойти за ней = go back for it / go get it

It is related to the literal idea of going after it, but in normal usage it is an idiomatic and very common way to say go fetch.

Because за in this meaning requires the instrumental case.

The noun being referred to is мочалка, which is feminine, so the pronoun is the feminine form of it.

Instrumental forms of она:

• ею / ней

After prepositions, ней is the usual choice:

• за ней

So:

• пошла за ней = went to get it

Not:

• за её — incorrect here
• за неё — different case, different meaning

Because пошла fits a single completed action in a sequence.

пошла

This is the past tense of пойти (perfective). It often means set off / went as one whole event.

That works well in a story:

• Я забыла... и пошла...
• I forgot... and went...

шла

This would focus more on the process of walking / going:

• Я шла за ней = I was going to get it

ходила

This often suggests a round trip, repeated action, or a more general fact:

• Я ходила за ней = I went to get it (with a slightly different feel, often less about the exact moment of setting off)

So пошла is the most natural choice here.

Уже means already, by then, or at that point.

Here it emphasizes that by the time she went back for the washcloth, she was already in her pajamas.

So the feeling is something like:

• she had already changed
• it was late enough that she was in pajamas
• going back for the washcloth was a bit inconvenient or mildly annoying

It often adds a small emotional nuance, not just a time fact.

It is prepositional singular after в.

Base form:

• пижама = pajamas / pyjamas

Form after в for location or state:

• в пижаме = in pajamas / wearing pajamas

Russian often uses в + prepositional for what someone is wearing:

• в пальто = in a coat
• в шапке = in a hat
• в пижаме = in pajamas

So this is a normal way to describe someone’s clothing or appearance at that moment.

Russian often does not need a separate verb like was in this kind of sentence.

The phrase уже в пижаме works as a description of the speaker’s state during the action:

• пошла за ней уже в пижаме = went to get it already in pajamas

Russian is very comfortable attaching this kind of phrase directly to the action, without adding была.

If you said something with была, it would usually sound like a different structure, not the most natural phrasing here.

The word order is fairly natural, but the end of the sentence gets emphasis.

• Я забыла мочалку в ванной и пошла за ней уже в пижаме.

The final part, уже в пижаме, is the detail being highlighted. It is the new or slightly striking information.

Russian word order is flexible, so you could move things around for emphasis, for example:

• Я уже в пижаме пошла за ней.
• За ней я пошла уже в пижаме.

But the original sounds natural and storytelling-like.