That's crap. Your GP is useless! After having a baby is prime time for thyroid issues and the fact that you are describing textbook symptoms, she should be getting you the blood tests FFS.
I also had 9 months of being fobbed off with talk of PND, the aches and pains were just "using muscles I wasn't used to" carrying a baby around and I was merrily given anti-depressants too, after DS1 was born.
I went to see my GP 3 times, each time describing my many textbook symptoms, telling her it felt like when I had Glandular Fever as a teen (which is associated with thyroid problems) that my mum said it sounded like her thyroid problem (Hashimoto's is hereditary) and that I couldn't even walk to the end of my street without stopping in agony, all told while in tears and struggling to get a sentence out - still she didn't test my thyroid 
When I had an allergic reaction to the ADs luckily the GP was away and I saw a locum - he ordered thyroid tests and called me in immediately with the results, saying "you must be feeling very poorly indeed" as I had virtually no thyroid function - he was amazed I was still functioning! I just burst into tears.
Been on meds for 18 years now. I dread to think what would have happened if that locum hadn't tested me. I think I'd go private knowing what I know now, but at that time I didn't have the confidence or assertiveness to stand up for myself and insist on anything. I've since had similar with B12 deficiency - had to diagnose it myself online, GP said its unlikely to be that, but eventually tested and lo & behold, it was low.
It's so hard, as it's when you most need to be your own advocate that you least feel able to do it.
Could your DH or mum go with you to your next appointment? Sadly I find they listen to men more and if there's a witness to them refusing you tests they will feel much more likely to be sympathetic.
You can order your own blood tests for £30-50 from various places online as a last resort - Medichecks and Blue Horizon spring to mind. You still need your GP to take the results seriously in order to prescribe meds but it could be worth it to get things moving if they won't listen.
I'm sorry you're suffering - hope that whatever it is you get to the bottom of it. 