Brief Answer:
May persist for weeks unfortunately.

Detailed Answer:
I read your question carefully and I understand your concern.

I think your doctor referred to what is called post concussion syndrome. It is a group of symptoms which may happen after mild head trauma, like headache, difficulty concentrating, fatigue etc.
Duration of the symptoms is very variable. It may last for several weeks, at times even for months, so it is not that surprising lasting for a week unfortunately. It has an important psychological component so stress may be a factor as well.
Given the type of hit that you took, I would say that it shouldn't last that long, about a couple of weeks. It is important also to rest, by which I don't mean simply physical but also mental rest. Avoid watching TV or reading for prolonged periods during the next few weeks, avoid confrontations. May still take Tylenol or Advil for the headache (Tylenol while not as effective is safer).

Symptoms which would be a reason for concern and require another doctor evaluation would be if headache goes increasing in intensity, nausea and vomiting, seizures, changes in behavior noted by those close to you, double vision or vision loss, motor weakness or numbness of the limbs, coordination issues etc. However complications usually occur in the first 24-48 hours, very unlikely at this stage unless you are under blood thinners or have some blood clotting condition.

I remain at your disposal for other questions.

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Brief Answer:
please read the detailed answer below.

Detailed Answer:
Flying is okay, have no worry about it.

As for yoga and treadmill....as I said before, rest is advised, exertions are not recommended. However, yoga helps with relaxation and might be beneficial if you avoid extreme positions, and concentrate more on relaxation and breathing exercises (I wish I was more specific but not a yoga expert). Some mild but not fast paced walking should be ok too.

Let me know if I can assist you further.

Regards

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