Brief Answer:
Information

Detailed Answer:
Hello and welcome,

You are good to be a concerned dad about this. Yes, it could be an autoimmune disorder, given this constellation of symptoms. I recommend that she see her doctor for a general physical and start with a complete blood count with differential (to check for occult infection), a sedimentation rate (sed rate) and C-reactive protein (to assess for inflammation - although it won't indicate the source of the inflammation but can be used to track degree of inflammation over time), and an autoimmune panel.

Autoimmune antibodies that can be tested for systemic (not organ specific) diseases are:
The list below includes some of the autoantibody tests that are used to identify systemic autoimmune disorders. These disorders may cause signs and symptoms associated with inflammation throughout the body.

Antinuclear Antibodies (ANA)
Antineutrophil Cytoplasmic Antibodies (ANCA)
Anti-Double Stranded DNA (anti-dsDNA)
Anticentromere Antibodies (ACA)
Antihistone Antibodies
Cyclic Citrullinated Peptide Antibodies (CCP)
Extractable Nuclear Antigen Antibodies (e.g., anti-SS-A (Ro) and anti-SS-B (La), anti-RNP, anti-Jo-1, anti-Sm, Scl-70)
Rheumatoid Factor (RF)

And these are examples of autoantibodies associated with certain systems or organs:

Cardiolipin Antibodies
Beta-2 Glycoprotein 1 Antibodies
Antiphospholipid Antibodies (APA)
Lupus anticoagulants (LA)
Endocrine/metabolic system
Smooth Muscle Antibodies (SMA)
Antimitochondrial Antibodies (AMA)
Liver Kidney Microsome Type 1 Antibodies (anti-LKM-1)
Kidney Anti-Glomerular Basement Membrane (GBM)
Muscles Acetylcholine Receptor (AChR) Antibodies
Thyroid autoantibodies

So here is what I would start with:
CBC with differential (looking for infection)
ESR (sed rate)
C-reactive protein (this and sed rate are for inflammation)
ANA (looking for lupus and other autoimmune antibodies)
RF (rheumatoid factor for rheumatoid arthritis)
I would do the above 2 if her health care system doesn't have a general autoimmune panel.

If the sed rate or C-reactive protein are elevated but no infection (per CBC) and the ANA and RF are normal, then I would either order further antibody tests or would refer her to a rheumatologist.

I hope this information helps. Good luck to her.

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Brief Answer:
Thoughts on this

Detailed Answer:
Typically, when we don't have a solid idea of what we are pursuing yet, we start with a general exam which should (given her headaches) include a preliminary neuro exam and exam of her abdomen.

At that time, the doctor should get blood work, and can get a plain X-ray of the shoulder and knee. Then an MRI would be the next step.

I do agree that if a cause for the headaches isn't apparent after an exam and blood work (and whatever information the X-rays provide), that a persistent headache should be evaluated with a head CT or MRI.

Regarding whole body CT (head, chest, abdomen, pelvis), that may be down the road, but need to start with the basics first (physical exam, blood work, etc).

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