Hello Kimbo - it sounds to me that you are wise to listen to your body and investigate the possibility of perimenopause (the time before periods stop for good, the time where hormones become unbalanced and symptoms can present) being a factor.
I am not sure why your GP will not run any blood tests until your periods have stopped for a year. It is definately the case that blood tests can be unreliable in determining whether we are in perimenopause because hormones go up and down so much, but I would have thought it would be useful to at least do one, if not a few. If you choose to get private tests, you would want to test FSH levels, which go up when we begin to skip ovulating so often and possibly your estrogen and progesterone levels, the NHS tend to only test the FSH. The other blood test that is often done, usually if periods start changing is to check thyroid levels, as this has an influence on our cycles as well.
There is a lot of information on this sight, lots to take in, but honestly I would consider speaking to your GP or a different one and stress that you really would like further investigation into your symptoms and the possibility of hormonal issues being part of them, especially considering your family history.