I'm sorry you're unwell. You need to follow sick day rules.
If you don't know what they are or are worried, you should phone 111 for advice and support.
Ask 111: Your ketones shouldn't rise above 3 mmol/l if you have insulin on board. At 0.6 you should be safe if you're still taking your insulin
I hope you feel better soon.
In the meantime, here is what I learnt on my DAFNE course. Sick day rules:
If your blood glucose is above 13mmol/L: Increase your usual insulin by 10%
If no response 2 to 4 hours, stay with the increase of usual insulin by 10% and give an extra dose of quick acting insulin (approximately 10% of total daily insulin) repeat every 2 to 4 hours.
https://www.northumbria.nhs.uk/sites/default/files/images/PIN451[1].pdf