Mi hermana pensaba que tenía una fractura, pero la radiografía mostró que solo era un esguince.

Pensaba is the imperfect, which often gives background information or describes an ongoing mental state in the past.

Here, Mi hermana pensaba que... means she thought/believed that she had a fracture. The idea is not that she had one single, sharply defined thought, but rather that this was her belief at the time.

If you said pensó, it would sound more like she had the thought at a particular moment. That is possible in some contexts, but pensaba is more natural here.

Because tenía describes the condition she believed she had.

In Spanish, when talking about an illness, injury, or state that someone is experiencing, the imperfect is very common if you are presenting it as an ongoing situation in the past. She believed that she had a fracture; it was not seen as a completed event.

Tuvo una fractura would usually sound more like she had a fracture as a completed past fact, often from the outside, not as part of what she thought at that moment.

Mostró is the preterite, used for a completed action.

The X-ray gave its result at a specific moment: it revealed what the injury really was. That is why mostró fits well.

So the contrast is:

• pensaba = background belief
• mostró = completed revelation/result

This imperfect + preterite contrast is very common in Spanish storytelling.

Era sounds more natural because it identifies the injury as a state/condition, not as a one-time event.

After a test or examination, Spanish often uses ser in the imperfect to say what something turned out to be:

• mostró que era un esguince
• resultó que era una infección

Fue un esguince is not impossible in all contexts, but here it sounds less natural. Era presents the diagnosis as the condition that existed.

Here la radiografía means the X-ray or the X-ray image/result.

In everyday English, we often say the X-ray showed..., and Spanish does the same with la radiografía mostró...

A learner might expect los rayos X, and that is also possible in some contexts, but la radiografía is completely natural when referring to the image or exam.

Because it refers to a specific X-ray: the one she had.

Spanish uses definite articles more often than English does. So where English might say X-ray showed..., Spanish often says the X-ray showed...

That is why la radiografía sounds normal.

• fractura = fracture, usually a broken bone
• esguince = sprain, an injury to a ligament, usually from twisting a joint

So this sentence contrasts a more serious suspected injury with a less serious one.

A native English speaker may also wonder whether esguince means strain. Usually it does not. A sprain is more specifically esguince.

Under current standard spelling, solo is normally written without an accent.

In the past, some people wrote sólo when it meant only, to distinguish it from solo meaning alone. Today, the usual recommendation is to write solo without the accent in both cases, unless there is real ambiguity.

So solo era un esguince is standard modern spelling.

Yes, you could, but the nuance is slightly different.

• solo era un esguince = it turned out to be just a sprain
• solo tenía un esguince = she only had a sprain

Both are correct here.
Era un esguince focuses more on the diagnosis/identity of the injury.
Tenía un esguince focuses more on what she had.

In this sentence, era un esguince sounds especially natural after mostró que...

The subject is not stated explicitly, but it is understood from the context.

It is basically referring to the injury / what she had / the problem. Spanish often leaves that kind of subject unstated when it is clear.

So the idea is something like:

• mostró que lo que tenía solo era un esguince

But Spanish usually does not need to spell all of that out.

Spanish often omits subject pronouns because the verb ending already tells you who the subject is.

• pensaba = she/I was thinking
• tenía = she/I had
• mostró = it/he/she showed
• era = it/he/she was

The context makes it clear that:

• mi hermana is the one who pensaba and tenía
• la radiografía is the one that mostró

Adding pronouns here would usually be unnecessary.

Yes, it sounds natural in Spain.

It is a very normal way to describe a medical misunderstanding:

• someone thought the injury was one thing
• a test showed it was something else

The vocabulary and grammar are standard and natural for Spain Spanish.