Se me metió una pestaña en el ojo y estuve un rato sin poder leer.

This is a very common Spanish pattern for something that happens to a person, often unintentionally or inconveniently.

• me marks the person affected: to me / on me
• se helps present the event as something that happened, rather than something someone deliberately did

So se me metió una pestaña en el ojo is roughly like:

• An eyelash got into my eye
• more literally: An eyelash got itself into my eye on me

It is similar in feel to expressions like:

• Se me cayó el móvil = My phone fell / I dropped my phone
• Se me rompieron las gafas = My glasses broke on me

Spanish often uses this kind of structure where English does not.

The base verb is meter, which usually means to put / to stick / to insert.

Here, Spanish uses the pronominal form meterse, which can mean to get into or to go into something. So:

• se metió ... en el ojo = got into the eye

In this sentence, it does not mean that someone actively put the eyelash there. It means it ended up there.

A similar alternative would be:

• Me entró una pestaña en el ojo

That also means an eyelash got in my eye, but meterse is very natural in this context.

Because the eyelash getting into the eye is seen as a single completed event.

• se me metió = it happened at a specific moment
• se me metía would suggest something habitual, repeated, or an action viewed as ongoing/background

Here the speaker is talking about one event: the eyelash got into the eye, and then as a result they could not read for a while.

Because it is the subject, and in Spanish the subject often comes after the verb, especially when:

• introducing new information
• describing something that happened suddenly
• reporting an event in a natural, spoken way

So in:

• Se me metió una pestaña en el ojo

the subject is una pestaña.

You could also say:

• Una pestaña se me metió en el ojo

and that is grammatically correct, but the original word order sounds more natural in everyday Spanish.

Because with body parts, Spanish usually prefers:

• an indirect object pronoun: me
• plus the definite article: el

So instead of saying my eye, Spanish often says the equivalent of the eye, because me already tells you whose eye it is.

That same pattern appears in:

• Me duele la cabeza = My head hurts
• Me lavé las manos = I washed my hands
• Se me metió una pestaña en el ojo = An eyelash got in my eye

Using mi ojo is not impossible in all contexts, but here el ojo is the normal choice.

Here it means eyelash.

• pestaña = eyelash
• ceja = eyebrow

So:

• una pestaña = an eyelash
• las pestañas = eyelashes

Because estuve presents the time as a finished stretch.

• estuve un rato sin poder leer = I was unable to read for a while

The phrase un rato gives the idea of a limited period, so the preterite estuve fits well.

By contrast, estaba usually gives background description or an ongoing state without focusing on its boundaries. In this sentence, the speaker is talking about a completed period of time, so estuve is the natural choice.

It means for a while, for a bit, or for some time.

It is a very common everyday expression, especially in spoken Spanish. It is intentionally vague: it does not tell you the exact length of time.

Depending on context, un rato might mean:

• a few minutes
• quite a while
• simply some time

Because after sin, Spanish normally uses an infinitive, not a conjugated verb.

So:

• sin poder leer = without being able to read

This is very natural Spanish.

Compare:

• sin comer = without eating
• sin dormir = without sleeping
• sin poder leer = without being able to read

English often uses a full clause like I couldn't read, but Spanish very naturally uses sin + infinitive to express the same idea.

Yes, that would also be possible, but the nuance is slightly different.

• Estuve un rato sin poder leer focuses on the period of time spent being unable to read.
• No pude leer durante un rato focuses more directly on the fact that reading was impossible for that period.

Both are understandable and natural, but the original sounds especially idiomatic because it describes the temporary state caused by the eyelash.

Yes. That is also natural.

• Me entró una pestaña en el ojo = An eyelash got in my eye
• Se me metió una pestaña en el ojo = very similar, also very natural

The version with meterse can feel slightly more like the eyelash ended up lodged in there or got itself in there, but in everyday use the two are very close in meaning.