Make sure you take your levemir, at least. Hope you are feeling better soon. What are your levels like? If they are high you may need some novorapid. Are you checking for ketones?
Your diabetes team should have told you about "Sick Day Rules", but in case they haven't, as an example, here is what West Suffolk Hospital recommends for people with type 1 diabetes. http://www.diabetesuffolk.com/managingdiabetes/Sick day rules.htm
When my OH was ill with vomiting ( he is not diabetic) the pharmacist advised sipping flat standard coke - it apparently has all the electolytes you need to re-hydrate - I don't know if that applies to the diet variety - maybe call the pharmacy.
But you definitely need to keep taking the insulin. Can you contact your GP or DSN for advice ?