Se sintió avergonzada ayer.

Because the verb here is sentirse, which means to feel in the sense of someone’s emotional or personal state.

• sentir = to feel, sense, notice
• sentirse = to feel, to feel oneself, to be feeling

So:

• Sintió frío = He/She felt cold
• Se sintió avergonzada = She felt embarrassed

In this sentence, se is the reflexive pronoun that goes with sentirse.

Sintió is the preterite form, used for a completed action or state in the past.

Since the sentence includes ayer (yesterday), Spanish naturally uses the preterite here to show that this feeling happened at a specific time in the past.

• se sintió avergonzada = she felt embarrassed
• se siente avergonzada = she feels embarrassed
• se sentía avergonzada = she was feeling / used to feel embarrassed

So sintió fits a finished past event.

This is a stem change in the preterite of sentir.

The infinitive is sentir, but in some forms of the preterite, the stem changes from e to i:

• sentí
• sentiste
• sintió
• sentimos
• sentisteis
• sintieron

So sintió is just the correct third-person singular preterite form.

Because avergonzada is an adjective, and it must agree with the person being described.

Here, the sentence refers to a feminine singular person, so the adjective is feminine singular too:

• avergonzado = embarrassed, masculine singular
• avergonzada = embarrassed, feminine singular

If the person were male, it would be:

• Se sintió avergonzado ayer.

Spanish often leaves out subject pronouns because the verb ending usually makes the person clear enough.

Sintió can mean:

• he felt
• she felt
• you (formal singular) felt

So the exact subject usually comes from context. Spanish does not need to say ella unless it is needed for emphasis or clarity.

• Ella se sintió avergonzada ayer = possible, but not necessary
• Se sintió avergonzada ayer = very natural

Yes, in the right context it could mean you if the speaker is addressing usted.

The form sintió is third-person singular, and that is also the form used with usted.

So depending on context, Se sintió avergonzada ayer could mean:

• She felt embarrassed yesterday
• You felt embarrassed yesterday (formal, addressing a woman)

But if the meaning shown to the learner is she felt embarrassed yesterday, then that is the intended reading here.

After sentirse, Spanish normally uses an adjective to describe how someone feels.

Examples:

• se sintió feliz
• se sintió mal
• se sintió cansada
• se sintió avergonzada

So avergonzada describes her emotional state. It works like embarrassed in English.

The accent mark shows the correct stress and helps distinguish the form.

Sintió is pronounced with the stress on the final syllable: sin-TIÓ.

In writing, many Spanish preterite third-person forms need this written accent:

• habló
• comió
• vivió
• sintió

So the accent is a normal part of the correct spelling.

Yes, ayer can move around. Spanish word order is flexible.

All of these are possible:

• Se sintió avergonzada ayer.
• Ayer se sintió avergonzada.
• Se sintió ayer avergonzada. (less common / less natural in many contexts)

The version with ayer at the end is very natural and neutral.

These forms are similar, but they are not exactly the same.

• se sintió avergonzada focuses on how she felt
• estuvo avergonzada focuses more on being in that state for a period
• estaba avergonzada gives background or an ongoing past state

Compare:

• Se sintió avergonzada cuando lo vio. = She felt embarrassed when she saw him.
• Estaba avergonzada mientras hablaba. = She was embarrassed while she was speaking.

So sentirse + adjective is a very common way to talk about emotions.

It is a correct and common word, yes. Another very common option is avergonzado / avergonzada with sentirse.

You may also see related expressions depending on context:

• tener vergüenza = to feel ashamed / to feel embarrassed
• dar vergüenza = to cause embarrassment
• qué vergüenza = how embarrassing / what a shame

But for the structure in this sentence, sentirse avergonzada is completely natural.

Not when the verb is conjugated like this.

With a normal conjugated verb, the reflexive pronoun goes before the verb:

• Se sintió avergonzada

It can go after the verb only with:

• an infinitive: va a sentirse mejor
• a gerund: está sintiéndose mejor
• an affirmative command: siéntete mejor

So in this sentence, se sintió is the correct order.