As an employment law adviser in an advice centre I can tell you that this is a situation which your employer should never have allowed to arise, especially as they appear to have recognised your situation and done something about it. They now need to do the rest.
As someone has already guessed, this is covered by legislation. You have been provided with a room to inject yourself, but if your colleagues really cannot stand the sight of blood, is there a reason why you cannot use the same room for testing your blood sugar? Are 'tied' to your desk/workstation and not allowed to leave it, as often is the case in call centres: could it affect your productivity and affect your pay or a bonus payment?
The first rule in any situation like this is Be Reasonable. It is the case that some people really do have a phobia - I know someone who really will faint at the sight of a needle and he is scientist! Is it perhaps the case that one of your colleagues is genuinely upset by what, to us, is a routine thing but you could argue that such a phobia is perhaps also covered by the DDA, so both parties must consider each other.
If you do not feel you can talk effectively to the people who are making you feel hounded then go to your boss and ask for help. S/he must take action and if, in the extreme, you find you cannot work there any more you may well have a claim for unfair dismissal. If your employer does not want to become involved then you may want to take advice from a solicitor, which will probably cost you, or an advice centre which is normally free. Try Googling 'advice centres' and see if you can find a local one - remember that not all advice centres are CABs; there are hundreds of independent ones, many more than there are CABs - or if you have a Union, try them.
Best of luck.
I think its disgusting you're having someone complain about you pricking!
