Ég gleymdi sólkreminu heima og húðin mín varð rauð á ströndinni.

Because the verb gleyma takes the dative case in Icelandic.

The base noun is sólkrem = sunscreen.
It is a neuter noun.

• sólkremið = the sunscreen in the nominative/accusative
• sólkreminu = the sunscreen in the dative

Since Icelandic says að gleyma einhverju = to forget something, with that something in the dative, the sentence uses:

• Ég gleymdi sólkreminu = I forgot the sunscreen

This is a very common thing learners have to memorize: some verbs require a specific case, and gleyma is one of them.

Because heima means at home, while heim means homeward / to home.

Icelandic often distinguishes between:

• location: where something happens
• direction: where someone is going

So:

• heima = at home
• heim = home / to home

In this sentence, the sunscreen was forgotten at home, so the location form is needed:

• Ég gleymdi sólkreminu heima = I forgot the sunscreen at home

If you were talking about motion, you might see:

• Ég fór heim = I went home

In Icelandic, possessives like minn / mín / mitt often come after the noun, especially in neutral, ordinary statements.

So:

• húðin mín = my skin

This is the most natural wording here.

You can place the possessive before the noun in some contexts, but that often sounds more emphatic, contrastive, or stylistically marked. For a normal sentence, húðin mín is what learners should expect.

Also note that húðin already means the skin, so literally húðin mín is something like the skin of mine, which is a very common Icelandic pattern.

Because verða means to become / to get, while vera means to be.

The sentence is describing a change of state:

• the skin became red

So Icelandic uses:

• húðin mín varð rauð = my skin became red

If you said var rauð, that would mean was red, describing a state rather than the change into that state.

Compare:

• Húðin mín var rauð. = My skin was red.
• Húðin mín varð rauð. = My skin became red.

Because Icelandic adjectives must agree with the noun in gender, number, and case.

The noun here is húðin:

• singular
• feminine
• nominative

So the adjective must also be:

• singular
• feminine
• nominative

That gives:

• rauð

Compare the nominative singular forms:

• masculine: rauður
• feminine: rauð
• neuter: rautt

So:

• húðin mín varð rauð = correct, because húð is feminine

Because á is the preposition needed here, and with location it takes the dative.

The phrase means on the beach or at the beach.

The noun is strönd = beach, a feminine noun.
Its definite dative singular form is:

• ströndinni

So:

• á ströndinni = on the beach / at the beach

This is similar to the location/direction distinction with some prepositions in Icelandic:

• á + dative = location, on
• á + accusative = motion onto something

Here it is location, so dative is used.

Gleymdi is the past tense of gleyma = to forget.

In this sentence:

• Ég gleymdi = I forgot

This form is:

• 1st person singular, past tense
• but it is also identical in form to 3rd person singular past for this verb

So both of these are possible:

• Ég gleymdi = I forgot
• Hún gleymdi = She forgot

That is normal in Icelandic verb conjugation: some persons share the same form.

It is a compound noun:

• sól = sun
• krem = cream

So sólkrem literally means sun cream, which in natural English is often sunscreen or sun lotion, depending on context.

Compound nouns are extremely common in Icelandic, and learning to recognize their parts is very helpful.

Because Icelandic marks both:

1. the definite article (the)
2. grammatical case

Unlike English, Icelandic usually attaches the to the end of the noun.

Examples from the sentence:

• sólkrem = sunscreen

• sólkreminu = the sunscreen in the dative

• húð = skin

• húðin = the skin in the nominative

• strönd = beach
• ströndinni = the beach in the dative

So those endings are not random: they tell you important grammar information.

Yes, it is very natural.

The basic structure is:

• Ég gleymdi sólkreminu heima
• og húðin mín varð rauð á ströndinni

This is straightforward, neutral word order. Icelandic does have some word-order flexibility, but this sentence is a very standard way to say it.

A learner should notice that Icelandic often keeps things quite close to English in simple main clauses:

• subject
• verb
• object/complements

Even so, the cases and verb choices carry a lot of the grammatical meaning.

Literally, rauð means red.

In this sentence, though, the meaning is clearly that the skin turned red from the sun, so in context it strongly suggests sunburned or red from sunburn.

So:

• literal meaning: my skin became red
• natural interpretation: my skin got sunburned / turned red

Icelandic often uses ordinary descriptive words like rauður / rauð / rautt where English might choose a more specific word depending on context.