Blood tests will give the doc and you whatever information the doctor requests. If he includes things like Sed Rate or other specific tests for autoimmune diseases and tests for various vitamin deficiencies, you may well get somewhere. But, it can also be spinning wheels. What was his reason for not referring you to a specialist? Does he discount what you're telling him or do you know his thinking? Does he have a theory as to what's happening?
Perhaps if you mention your thoughts about autoimmune disorders or vit deficiency he will begin thinking in that direction. At least, ask him to order the more specific testing to ck it out. He may learn something in the process.
Then, a second request for referral is in order.

Does your insurance require a referral to a specialist to cover it? Sometimes we can make appts on our own, depending on the coverage. I'm able to do that, in fact that's how I got to Mayo neurology. I called and explained my situation and got an appointment.
I hope this works for you and he adds some tests. It's interesting how we have to help our doctors, especially if they're not extremely inquisitive. your situation can be too big a challenge for some, but you may be able to get him to work with you on this.....Go for it and do well. You are in control of your life, even tho it may seem out of control at this time. We have to advocate for ourselves, and I found with some of the wonky disorders and diseases, especially autoimmune, doctors can be overwhelmed....too many unknowns. So, you lead him to help you get answers from bloodwork or help you find answers from others. Bless you on this journey. You will find answers! elizabeth

He didn't discuss what the specific tests would be for, just that I'd need to have further blood tests. I've got the blood test form which is requesting the following: Blood film, ESR, Full blood count, creatine kinase, CRP, Liver, TSH, 25-hydroxy vitamin D, Anti nuclear antibody and IgG A M & Electrophoresis.