My sympathy - I have had this nausea a few times and also annovulatory cycles that did seem to increase symptoms, or at least the nausea and fatigue. For me, I am not so sure it is low estrogen, but high. It doesn't really matter in the end, you want to get rid of the symptoms or at least ride them out.
I am not on HRT and thankfully the symptoms are not lasting, they are moving and mostly daily, albeit subtle at times. There is a pattern appearing and I guess my body is in a new cycle at the moment, about six months ago, things were swinging about much more wildly - I have to agree that considering the idea that HRT is creating wider swings as your own hormones are still fairly active seems logical.
I don't have any advise about that, except that you have good support from those that have been in exactly your situation and considering the Pill seems a good next step.
Personally I am convinced by anxiety/depressed mood is due to being stressed for the last few years and having a rather tired system. The adrenal glands do a lot more work in producing hormones around this time and beyond and if they aren't functioning at optimum, it makes sense that mood would be a key symptom in this case. I am trying so hard to calm my whole system with rest, positive thought, supplements and excercise and for now, things are OK ish.
Wishing you well at the GP's