Hi. I don't know why your muscles are aching, but I can say that high blood sugars even not outrageously high ones, like hovering around 11 mmol/l, makes my body ache and makes me constantly fatigued. I think a first base is to get your control sorted out. It might not be the answer - but it might, and it's something that needs to happen for your general wellbeing anyway.
That's a bit hard when you don't have bolus insulin. My reaction to the idea of starting a T1 on basal only and resigning them to having to go low carb just to get middling to poor control is that it is cruel and unusual. I just cannot comprehend why this has happened this way for you.
Anyway, I understand we are often at the mercy of our doctors, but if there is any way you can accelerate this process it would be a good thing. Once you have bolus insulin you have at least the basic tools to provide control (with a lot of adjustment, likely), plus you can also up your carbs and test whether it's the low carb diet that your body does not like. I'm sure you've picked up that self education is key to success with diabetes, if you haven't picked up a good book such as Using Insulin by John Walsh I'd highly recommend it. Good luck and I hope the aching resolves soon.