קבעתי תור לבדיקה אצל רופאת המשפחה, כי אני רוצה לדעת אם אני צריכה גם חיסון.

Yes. In this context, קבעתי תור is the normal everyday way to say I made / booked an appointment.

A few useful points:

• קבעתי = I set / arranged / scheduled
• תור can mean turn, queue/line, or appointment, depending on context

So here, with a doctor and a checkup, תור clearly means appointment.

Examples:

• קבעתי תור לרופא = I booked a doctor’s appointment
• יש לי תור מחר = I have an appointment tomorrow

The prefix ל־ here means for.

• בדיקה = checkup, examination, test
• לבדיקה = for a checkup / for an examination

So תור לבדיקה means an appointment for a checkup.

This is very common in Hebrew: a noun with ל־ can show the purpose of the appointment.

For example:

• תור לייעוץ = an appointment for consultation
• תור לבדיקה = an appointment for an examination

אצל is very commonly used in Hebrew for being at someone’s place, and by extension with a doctor, hairdresser, lawyer, etc.

So:

• אצל הרופא = at the doctor’s / with the doctor
• אצל רופאת המשפחה = with the family doctor

This sounds very natural in Hebrew.

By contrast:

• עם simply means with, but it is less idiomatic here
• ל־ can also appear in some appointment expressions, but אצל emphasizes the professional you are going to see

Because רופאת המשפחה is a construct phrase (in Hebrew: סמיכות).

The basic noun is:

• רופאה = a female doctor

But when it is followed by another noun in a construct phrase, it changes form:

• רופאת המשפחה = the family doctor literally doctor of the family

This change from ־ה to ־ת is very common in feminine singular nouns in construct.

Compare:

• מורה = teacher
• מורת הדרך = the guide / instructor

That is how definiteness works in Hebrew construct phrases.

In רופאת המשפחה:

• רופאת = doctor of ...
• המשפחה = the family

When the second noun in a construct phrase is definite, the whole phrase becomes definite.

So:

• רופאת משפחה = a family doctor
• רופאת המשפחה = the family doctor

English speakers often expect both words to show definiteness, but Hebrew does not work that way in this structure.

Yes, the speaker is female.

The clearest clue is:

• צריכה = needs (feminine singular)

A male speaker would say:

• צריך = needs (masculine singular)

Also, רופאת shows that the doctor is female.

One interesting detail:

• רוצה is spelled the same in unpointed Hebrew for both masculine and feminine singular
• so in writing, רוצה alone would not prove the speaker is female
• צריכה does prove it

כי means because.

It introduces the reason:

• קבעתי תור... כי... = I made an appointment... because...

This is one of the most common ways to connect two clauses in Hebrew.

So the structure is:

• main statement: קבעתי תור לבדיקה אצל רופאת המשפחה
• reason: כי אני רוצה לדעת אם אני צריכה גם חיסון

Yes, and this is very natural Hebrew.

Literally:

• רוצה = want
• לדעת = to know

But in context, רוצה לדעת אם... often means:

• I want to know whether...
• I want to find out if...

So even though the literal verb is to know, the natural English meaning can be find out.

Here אם means if / whether in an indirect yes-no question.

So:

• אני רוצה לדעת אם... = I want to know if / whether...

This is very common after verbs like:

• לדעת = to know
• לשאול = to ask
• לבדוק = to check

For learners, an important distinction is:

• אם often introduces an embedded question: I want to know if...
• האם is often used in more formal yes-no questions

In this sentence, אם is the normal everyday choice.

Because חיסון here is indefinite: a vaccine / any vaccine, not the vaccine.

In Hebrew, את marks a definite direct object.

So:

• אני צריכה חיסון = I need a vaccine
• אני צריכה את החיסון = I need the vaccine

Since the speaker is asking whether she needs some vaccine in addition, not a specific already-known vaccine, חיסון appears without את and without ה־.

גם means also / too.

So:

• גם חיסון = also a vaccine

The idea is that the speaker may need not only the checkup, but an additional thing as well: a vaccine.

In Hebrew, גם is usually placed right before the word or phrase it modifies. Here it modifies חיסון, so it means:

• whether I also need a vaccine

If you move גם, the emphasis can change slightly.

Only the gender-marked words would change.

If the speaker were male:

• קבעתי תור לבדיקה אצל רופאת המשפחה, כי אני רוצה לדעת אם אני צריך גם חיסון.

Change:

• צריכה → צריך

If the doctor were male:

• קבעתי תור לבדיקה אצל רופא המשפחה, כי אני רוצה לדעת אם אני צריכה גם חיסון.

Change:

• רופאת → רופא

If both were male:

• קבעתי תור לבדיקה אצל רופא המשפחה, כי אני רוצה לדעת אם אני צריך גם חיסון.

This sentence is a good example of how Hebrew shows gender in both nouns and predicates.