Dr's that do this annoy me. They throw everything at the issue and see what sticks. It's an easy way to figure out what's wrong without spending time asking more in depth questions, and assessing the situation.
Having trouble sleeping? Oh well lets do a sleep study. Feeling tired? Yup I thinki I feel a goiter, better get and ultrasound of that.
Ok so if your sleep is of poor quality or not enough you are going to be consistently tired.
Did he run through these questions
Do you snore?
When you wake do you feel rested?
Do you have jumpiness when you sleep?
Do you ever wake up gasping?
Do you wake up frequently during the night?
How many hours a night do you sleep?
Do you nap every day?
This assessment gives me an idea of what's going on, and then I can decide based on this, and other things like weight gain/loss, body habitus, family history if it truly is a sleep study time, or if you just need to clean up your sleep hygiene.
Thyroid levels should be checked, and again look at weight gain/loss, increase/decrease in body hair. Hot or Cold all the time? These all indicate if there is thyroid issue. The Ultrasound may or may not be expensive depending on what your insurance plan is. Some cover them well others not so much.
I would start with the lab work and see what the results are. I would also look into the ultrasound, if you do have a goiter, then it should be taken care of before you have serious problems. Thyroid cancers are common in women in their 30-40's. They are also cureable, so don't panic.
Tell your Dr frankly about your concerns of costs. Some of them just don't get it, until you say wait a second. This is going to cost me money I don't have.
If you think you need meds with psych then obviously go to the appropriate person, many do not do both anymore though, therapy and meds. If your PCP is adept and knowing meds, and comfortable ordering them maybe a therapist is all you need. I do agree that the same AD and same AD dose for 15 years is probably not effectively treating your depression. Does your PCP do a yearly depression screening?
PM me if you want some other ideas.