El ruido de la calle me dio un susto, pero luego sentí un gran alivio al ver que no pasaba nada.

Both are correct, but dar un susto is a very common and natural Spanish expression for a sudden fright.

• El ruido me dio un susto = the noise gave me a scare / startled me
• El ruido me asustó = the noise scared me

The version with dar un susto often feels a bit more idiomatic and can suggest a brief, sudden shock.

Here, me is an indirect object pronoun meaning to me.

Literally, the structure is:

• El ruido = the noise
• dio = gave
• me = to me
• un susto = a fright

So word for word, it is something like The noise gave a fright to me.

Spanish often uses this pattern with dar:

• me dio miedo = it gave me fear
• me dio pena = it made me feel sad / sorry
• me dio rabia = it made me angry

Because sentir and sentirse are used differently.

• sentir + noun = to feel something
  
  • sentí alivio = I felt relief
• sentirse + adjective/adverb = to feel in a certain state
  
  • me sentí aliviado = I felt relieved
  • me sentí mejor = I felt better

So in this sentence, sentí un gran alivio is correct because alivio is a noun.

Grande becomes gran before a singular noun:

• un gran alivio
• una gran idea

In many cases, gran + noun sounds more natural and slightly more figurative or emphatic than grande after the noun.

So:

• un gran alivio = a great relief, very natural
• un alivio grande = grammatical, but less natural here

Al + infinitive is a very common Spanish structure meaning:

• when
• upon
• on doing something

So:

• al ver = when seeing / on seeing
• al llegar = when arriving
• al entrar = when going in

In this sentence, al ver que no pasaba nada means when I saw that nothing was happening / that nothing was wrong.

They describe completed events in the story.

• me dio un susto = the scare happened at a specific moment
• sentí un gran alivio = the feeling of relief came at a specific moment

The preterite is typical for events that move the story forward.

So the sequence is:

1. the noise startled me
2. then I felt relief

Both are seen as completed reactions.

This is about nuance.

• no pasó nada = nothing happened
• no pasaba nada = nothing was happening / nothing seemed to be going on / nothing was wrong

Here, after al ver, the imperfect pasaba presents the situation as the speaker observed it at that moment. It sounds like: I looked, and everything was fine; nothing was going on.

Also, no pasa nada is a very common Spanish expression meaning:

• it’s nothing
• nothing’s wrong
• don’t worry
• nothing happened

So vi que no pasaba nada or al ver que no pasaba nada is very natural.

Because Spanish normally uses negative concord.

That means multiple negative words can appear together in the same sentence, where English usually only uses one.

So:

• no pasaba nada = nothing was happening
• no vi a nadie = I didn’t see anyone
• no tengo nunca tiempo = I never have time

If the negative word comes before the verb, then no is usually not needed:

• Nada pasaba

But in this sentence, nada comes after the verb, so no is required: no pasaba nada.

De la calle tells you the source of the noise: it is the noise coming from the street.

So:

• el ruido de la calle = the noise from the street / the street noise

This is a very common Spanish pattern:

• el olor de la cocina = the smell from the kitchen
• la luz del sol = the light of the sun / sunlight
• el ruido del tráfico = the noise of the traffic

Because ruido often works like noise in English: it can be an uncountable or general idea.

• El ruido de la calle = the street noise

If you said los ruidos de la calle, that would suggest different individual sounds or noises coming from the street.

So the singular here is the most natural choice if you mean the general noise as a whole.

Because they follow different spelling rules.

• sentí needs an accent mark to show the stress on the last syllable: sen-tí
• dio does not take an accent because it is treated as a one-syllable word in standard spelling

So:

• sentí = accent needed
• dio = no accent

This often surprises learners, because dio may look like it has two syllables, but in normal Spanish spelling it is considered one.

Yes. In this sentence, luego and después are both possible.

• pero luego sentí...
• pero después sentí...

Both mean but then / but afterwards.

In Spain, luego is very common in everyday speech and writing. The choice here is mostly stylistic, not a big grammar difference.