Jag har ont i axeln, så jag orkar inte bära väskan.

Because ha ont is a very common Swedish expression for feeling pain. Literally it looks like have pain, but that is just how Swedish normally says it.

So:

• Jag har ont i axeln = I have pain in my shoulder / My shoulder hurts
• Hon har ont i ryggen = Her back hurts

Another common pattern is det gör ont = it hurts.

So both of these are natural:

• Jag har ont i axeln
• Det gör ont i axeln

With pain in a body part, Swedish usually uses ont i + body part.

Examples:

• ont i huvudet = a headache / pain in the head
• ont i ryggen = back pain
• ont i benet = pain in the leg

So i is the normal preposition here, even if English might phrase it differently.

Swedish often uses the definite form for body parts when it is already obvious whose body part is meant.

So:

• Jag har ont i axeln literally looks like I have pain in the shoulder
• but it naturally means I have pain in my shoulder

This is very common in Swedish. The same thing happens with other body parts:

• Jag tvättar händerna = I wash my hands
• Hon bröt armen = She broke her arm

You can say min axel, but in this sentence axeln sounds more natural.

Orka means something like:

• have the energy to
• have the strength to
• be up to
• sometimes manage to, especially because of tiredness, pain, or lack of energy

So jag orkar inte bära väskan is not just I cannot carry the bag in a neutral sense. It suggests that the speaker lacks the strength, energy, or physical ability at that moment.

Compare:

• Jag kan inte bära väskan = I cannot carry the bag
• Jag vill inte bära väskan = I do not want to carry the bag
• Jag orkar inte bära väskan = I do not have the strength/energy to carry the bag

After orka, Swedish normally uses the infinitive without att.

So:

• Jag orkar inte bära väskan
• not Jag orkar inte att bära väskan

This is similar to several other common verbs that are followed directly by an infinitive, such as:

• kan bära
• vill bära
• måste bära
• ska bära

Because in a main clause, Swedish usually puts inte after the finite verb.

Here, the finite verb is orkar, so the order is:

• jag orkar inte bära väskan

This is standard Swedish word order.

A useful comparison:

• Main clause: Jag orkar inte bära väskan
• Subordinate clause: ... eftersom jag inte orkar bära väskan

So in subordinate clauses, inte usually comes before the finite verb.

Because så here is a coordinating conjunction meaning so, therefore, or as a result. It joins two main clauses.

That means the second clause keeps normal main-clause word order:

• Jag har ont i axeln, så jag orkar inte bära väskan

The subject jag comes before the verb orkar.

Compare that with därför, which is not used the same way:

• Jag har ont i axeln. Därför orkar jag inte bära väskan.

After därför at the start of a clause, you get inversion:

• Därför orkar jag...

But after så, you do not.

Väskan is the definite form, meaning the bag. Swedish uses the definite form when the bag is specific and known from the situation.

So this sentence suggests a particular bag:

• the bag the speaker has with them
• the bag both people already know about
• the bag that needs to be carried

If you said en väska, it would sound more like a bag, not a specific one.

Also, note how Swedish marks definiteness at the end of the noun:

• en väska = a bag
• väskan = the bag

Yes. Min axel gör ont is also correct and natural.

There is a small difference in focus:

• Jag har ont i axeln focuses more on you and the pain you feel
• Min axel gör ont focuses more directly on the shoulder itself

In everyday Swedish, both are common.

So these are both good:

• Jag har ont i axeln, så jag orkar inte bära väskan
• Min axel gör ont, så jag orkar inte bära väskan

The comma is natural here because the sentence contains two full main clauses:

• Jag har ont i axeln
• så jag orkar inte bära väskan

In Swedish, a comma before så in this kind of sentence is common and fully correct. In shorter or simpler sentences, people sometimes leave commas out, especially in informal writing, but here the comma helps readability.

So the version with the comma is a good model to follow.