The symptoms of low cortisol, or hypoadrenalism, include:
Mental and psychological ailments such as depression
Faintness and dizziness
Weakness and fatigue
Heart palpitations
Emotional hypersensitivity
Inability to cope with stress
Social anxiety
Muscle weakness
Headache, scalp ache, or general body ache
Severe or dull lower back pain
Extremely sensitive skin
Nausea, diarrhea, and vomiting
Abdominal pain and hunger pain despite an empty stomach
Extreme craving for salty foods
Anxiety and jitters
Clumsiness and confusion
Motion sickness
Insomnia and dark circles under the eyes
Low bladder capacity and symptoms of IBS
Irregular or non-existent menstrual period
So you need to get the tests I mentioned above. I agree with Rios that you need hormone testing, including estradiol, pregnenelone, testosterone, and progesterone. Of course the cortisol issue needs to be addressed, even before thyroid.
You can get some useful info from the following link. I highly recommend reading at least the first two pages, and more if you want to get into the discussion and scientific evidence for all that is recommended. Note especially Recommendation no. 16, on page 14, which states, " Central or secondary hypothyroidism is frequently part of a more complex hypothalamic
or pituitary disorder. This requires a complete evaluation and biochemical testing of all pituitary hormones and dependent organs. In case of suspected or proven cortisol deficiency of either central or adrenal origin, it is important to defer any thyroid hormone replacement until prior adequate correction of hypocortisolism."
http://www.thyroiduk.org.uk/tuk/TUK_PDFs/diagnosis_and_treatment_of_hypothyroidism_issue_1.pdf
Have you had an antinuclear antibody (ANA) blood test yet?
You mentioned you also suffer from PCOS. Many of your symptoms can also be improved with some progesterone treatment such as a cream or bioidentical oral progesterone. Of course, getting your adrenal issues under control, then your thyroid ailment treated will hopefully control most of your symptoms. Btw, IMHO, your doctor is in the wrong...a goiter is a CLEAR indicator that your thyroid is not functioning properly...get a new doctor before you get worse!!
Regarding your thyroid test results, here is a quote from an excellent thyroid doctor. "The free T3 is not as helpful in untreated persons as the free T4 because in the light of a rather low FT4 the body will convert more T4 to T3 to maintain thyroid effect as well as is possible. So the person with a rather low FT4 and high-in-range FT3 may still be hypothyroid. However, if the FT4 is below 1.3 and the FT3 is also rather low, say below 3.4 (range 2 to 4.4 at LabCorp) then its likely that hypothyroidism is the cause of a person's symptoms."
For your doctor to say that you are likely hypothyroid, and ignore all those symptoms that relate to hypothyroidism, and then refuse to treat you until your labs were out of range, is just ridiculous. A good thyroid doctor will treat a hypothyroid patient clinically, by testing and adjusting Free T4 and Free T3 as needed to relieve symptoms without being influenced by resultant TSH levels. Symptom relief should be all important, not just test results.
In view of your doctor's statement, why did he not address the cortisol test result that was out of range? Even though you need thyroid med your severe cortisol deficiency needs to be addressed first.
So I recommend that you call the doctor and ask about a prescription for hydrocortisone, adequate to get your cortisol level to optimal. Once on adequate hydrocortisone your cortisol will change fairly quickly. By that time you will be going back for followup tests. Along with Free T4, Free T3, you should request to be tested for Reverse T3, Vitamin D, B12, ferritin, and cortisol. You should also give the doctor the complete list of symptoms you provided above. We can give you lots of info to try and persuade the doctor to also start you on thyroid med at that time; however, based on experience to date, I am not very optimistic about that doctor. As an alternative, if you will tell us your location, perhaps we can give you the name of a doctor that has been recommended by other thyroid patients.
There is much to discuss, but first please tell us about the symptoms you mentioned.