Vorrei una cura che faccia effetto in fretta, perché domani devo lavorare.

Vorrei is the conditional of volere and is commonly used to sound polite, softer, and less direct.

• Vorrei una cura... = I’d like a treatment...
• Voglio una cura... = I want a treatment...

So voglio is not grammatically wrong, but it can sound more demanding. In a pharmacy or doctor’s office, vorrei is much more natural.

Here una cura means something like a treatment, a remedy, or a cure in a general medical sense.

It does not mean care in the emotional or caregiving sense here.

Depending on context, Italians might also say:

• una medicina = a medicine
• un farmaco = a drug/medication
• un rimedio = a remedy

Cura is a broad word, so in this sentence it means some kind of treatment that will help.

Una is the indefinite article, meaning a or an.

So una cura means a treatment, not the treatment.

That makes sense here because the speaker is asking for any suitable treatment, not referring to one specific treatment already known to both people.

Compare:

• una cura = a treatment, some treatment
• la cura = the treatment, a specific treatment

Here che is a relative pronoun meaning that.

It connects una cura with the description that follows:

• una cura = a treatment
• che faccia effetto in fretta = that works quickly / that takes effect quickly

So the structure is:

• una cura che... = a treatment that...

This is very common in Italian.

Because Italian often uses the subjunctive after a noun when you are talking about something wanted, hoped for, searched for, or not yet identified.

Here the speaker does not have a specific treatment in mind. They want some treatment that will work quickly. Since it is desired but not known, Italian uses the subjunctive:

• Vorrei una cura che faccia effetto...

If you were talking about a specific, known treatment, the indicative could be used:

• Conosco una cura che fa effetto in fretta.
  = I know a treatment that works quickly.

So:

• che faccia = desired / uncertain / not specific
• che fa = factual / known / specific

Fare effetto is an idiomatic expression meaning:

• to work
• to take effect
• to have an effect

So una cura che faccia effetto means a treatment that works or a treatment that takes effect.

A few examples:

• Questa medicina fa effetto subito. = This medicine works right away.
• Il farmaco non fa ancora effetto. = The medication hasn’t taken effect yet.

So you should think of fare effetto as a set expression, not translate it word by word too literally.

In fretta means quickly, fast, or in a hurry.

It is a very common everyday expression. In this sentence, it means the speaker wants the treatment to work quickly.

Other possibilities would be:

• rapidamente = rapidly
• velocemente = quickly
• presto = soon / early / quickly, depending on context

But in fretta sounds very natural and common in spoken Italian.

Perché always has an accent when written this way.

It can mean either:

• because
• why

In your sentence, it means because:

• ..., perché domani devo lavorare.
  = ..., because tomorrow I have to work.

The accent is required in standard spelling. You should learn perché as the normal written form.

Italian often leaves out subject pronouns because the verb ending already shows who the subject is.

• vorrei already means I would like
• devo already means I must / I have to

So:

• Vorrei... = I’d like...
• Domani devo lavorare. = Tomorrow I have to work.

You can add io for emphasis or contrast:

• Io devo lavorare, lui no.
  = I have to work, he doesn’t.

But in a normal sentence, leaving it out is more natural.

Because after dovere meaning must / have to, Italian uses the infinitive of the next verb.

So:

• devo lavorare = I have to work
• devi studiare = you have to study
• dobbiamo partire = we have to leave

This is just like English:

• I must work
• I have to work

You do not conjugate the second verb here. The modal verb devo is conjugated, and lavorare stays in the infinitive.

Yes. Both are possible.

• Domani devo lavorare puts emphasis first on tomorrow
• Devo lavorare domani sounds slightly more neutral in some contexts

Italian word order is fairly flexible, especially with time expressions like domani. The version in your sentence is very natural because it highlights the reason: tomorrow is the important point.

So the meaning stays basically the same, but the focus shifts a little.