lissaloo, I know where you stand. to some extend. I am 39 and have two children already. My situation is a bit different in that I am now with a new partner and we are ttc for his first child. But I do know exactly what you mean about wanting a 4th child as much as your first. That desire is not related to whether you are childless or already have 10, it is a yarning that engulfs you and takes over your life.
We haven't been ttc as long as you have, only since April, but because of the 'advanced age' (as they love to remind us), I can't help but feel concern about our chance to conceive.
Do make an appointment and if you feel you are belittled because of the fact you already have three children and you should stick at just being grateful, just make your point that it is your right to wish another child and to gain access to investigations. I was really nervous when I went to see my GP too. He does tend to intimidate me even though I have great faith in his judgment. Last time I saw him was when I asked for the pill and he told me that because of my 'advanced age' he would put me on the mini-pill because my chances of falling pregnant were now greatly reduced! So went there expected to fight for him to agree to blood test. I was also worried that he would pass a judgment on our decision to ttc since my new partner and I have only been together for a year. To my surprise, not only did he immediately agreed to the tests, but he also refer me to the FS without me even requesting it!
Our appt is in Feb and I am really grateful he decided to refer us (in Nov) as I am now at the stage that I need to know where we stand, even though we haven't yet contemplated what we would do if we are told our chances of pg naturally are seriously compromised.
I would definitely encourage you to make an appt with the doc, you have nothing to lose.