Deze bijwerking kan je benauwd maken.

Because bijwerking is a de-word: de bijwerking.

In Dutch:

• deze goes with de-words
• dit goes with het-words

So:

• deze bijwerking
• but dit medicijn if medicijn is being used as a het-word in that context

A good habit is to learn nouns together with their article:

• de bijwerking = the side effect

Bijwerking means side effect.

It is made up of:

• bij- = secondary, additional, incidental
• werking = effect / action / working

So bijwerking is literally something like an additional effect, which matches the idea of a side effect.

Here, je means you, but it is not the subject of the sentence.

The structure is:

• Deze bijwerking = subject
• kan = finite verb
• je = object
• benauwd maken = make ... short of breath / make ... feel tight-chested

So the sentence pattern is basically:

This side effect + can + you + make short of breath

That is why je comes after kan.

Yes, but it changes the tone a little.

• je = unstressed you, the normal everyday form
• jou = stressed you, used for emphasis or contrast

So:

• Deze bijwerking kan je benauwd maken. = neutral, most natural
• Deze bijwerking kan jou benauwd maken. = possible, but more emphatic, as if contrasting with someone else

In ordinary medical-style language, je is the more natural choice.

Because Dutch main clauses usually put the finite verb in second position.

Here:

• Deze bijwerking takes the first position
• so the finite verb kan must come second

The other verb, maken, is an infinitive, and infinitives usually go toward the end of the clause.

So:

• Deze bijwerking | kan | je benauwd maken

This is very common in Dutch with modal verbs like:

• kunnen
• moeten
• mogen
• willen

For example:

• Dit medicijn kan helpen.
• Je moet voorzichtig zijn.

Because after a modal verb like kunnen, Dutch uses the bare infinitive.

So:

• kan maken = can make
• not kan te maken

This is similar to English:

• can make
• not can to make

So the pattern is:

• kunnen + infinitive
• moeten + infinitive
• willen + infinitive

Examples:

• Ik kan komen.
• Je moet wachten.
• We willen gaan.

Benauwd can mean several related things, depending on context:

• short of breath
• tight-chested
• oppressed
• sometimes anxious or claustrophobic

In a medical sentence like this one, the most likely meaning is:

• short of breath
• or having a tight feeling in the chest

So this is a word whose exact English translation depends heavily on context.

This is a very common Dutch pattern:

iemand + adjective + maken
= to make someone + adjective

So:

• iemand moe maken = to make someone tired
• iemand zenuwachtig maken = to make someone nervous
• iemand benauwd maken = to make someone short of breath / tight-chested

Here:

• je = the person affected
• benauwd = the result/state
• maken = to make

So benauwd is not an adverb here; it is more like a result adjective describing what state the person ends up in.

It expresses possibility, not ability.

In this kind of medical warning, kan means:

• may
• can
• is capable of

So the idea is:

• this side effect may make you feel benauwd

This is a very common use of kunnen in warnings, instructions, and medical texts.

Yes. Dutch has several natural ways to express the same idea. For example:

• Deze bijwerking kan je benauwd maken.
• Je kunt door deze bijwerking benauwd worden.
• Deze bijwerking kan benauwdheid veroorzaken.

They are all natural, but they are slightly different in style:

• ... je benauwd maken sounds direct and clear
• ... benauwd worden focuses on what happens to the person
• ... benauwdheid veroorzaken is a bit more formal or medical

So the original sentence is a normal, idiomatic way to say it.