The number of points is somewhat irrelevant as long as they are all individually and collectively justified by the treatment approach. But a clear and well defined and justified approach is always better than chasing an array of symptoms/diagnoses.
I would suggest you generally start by reading our acupuncture treatment plan guidelines. While basic it may help to guide your treatment preparation.
As many things are interrelated in Chinese Medicine and we appreciate that and use this fact in the medicine, it can make the diagnostic process confusing. Generally you have to try to think of the progression of the disease - did they start getting worse after a longer protracted illness, or perhaps a defined period of stress, or did it appear suddenly…
Questions along those lines get you to the idea of what was there before what you are seeing now which makes it easier to see the progression and more defined interrelationships.
Then, generally, speaking you clear first and tonify later. So even if a person has spleen qi deficiency signs, unless all of their signs are true deficiency you wouldn’t start by tonifying. With heat signs, like the patient you are describing, you would at best lead to no improvement and at the worst, you would actually deepen their condition. But… you also cannot clear incredibly strongly if there are deficiencies, as opposed to a patient with full heat, for example, as that can make them worse, or at least not better. This is where understanding the patients history is critical in the process.
Generally speaking you take the most excess signs, clear them first and give the body time to come inline. As you are alluding to many things will start to take care of themselves once the largest imbalances are corrected. As the body starts to function more in balance, then you foster that, generally by movement and/or tonification.
In the simplest terms, clear heat first, move stagnation, then tonify if necessary.
As for your other question about addressing anxiety - if your diagnosis and approach is correct, yes, any symptoms in western terms that are arising from those imbalances should correct in due time.
If you would like to describe (1) what you are basing your diagnosis on in clinical terms, and/or (2) what points/techniques you are using - we may be able to offer more direct recommendations/guidance…