I don't know whether you have a 'right' under the NHS to get these tests but I would certainly ask your doc if you can see a specialist in order to discuss the pros and cons of getting them. And I would have thought that you DO have a right to have a discussion with a specialist for reassurance; but for that, I would try and get referred to a diabetes specialist nurse (DSN) rather than to a specialist in endocrinology. DSNs, in my experience, tend to be better at reassurance and practical empathy, while the endos tend to be experts in biomedical targets and chemistry.
I have found in the past in dealings with doctors that it can help to use the following buzz words: tell them that you want to be an active participant in your own care, and that a referral to a specialist would be a good way for them to provide a patient-centred response. Try and keep it positive (eg say you appreciate that they are being patient-centred - even if they aren't - rather than saying 'you aren't being patient-centred').
It might be worth pointing out to them that the more you know about diabetes and your own body, the better you will be able to look after yourself.
Personally I don't think you are asking for too much at all. You are asking for your concerns to be respected and taken seriously. That's fair enough I reckon.
