Hi, as I understand it, our bodies use keytones for fuel when it has no choice, ie. we starve it of other fuel, in your case vomitting, these are ok as long as they dont go too high coupled with high blood sugar, without testing equipment you wont know how high they are, you can buy the meter and keytone strips or wee strips on amazon (wee strips are rubbish imho) but will take a while to arrive and you want to know now, the only way is to visit A&E, you certainly do not need anyones permission to do this! it is very unlikely that you do in fact have a condition called ketoacidosis as this is caused by a lack of insulin and as a type 2 you probly have plenty but I have read on here folks with type 2 having it so its by no means certain.
My uneducated advice would be to visit A&E because it is the default response, you will probly be fine but for the sake of a boring sit in a germ infested room, you have nothing to lose and it could be important, I hope you get some help or better soon.
Emphasis on UNeducated.