Has my domestic oil run out?
no, it hasn't run out. yes, you have a problem somewhere else. no, we have no idea what it is. yes, you need to call for repair. and yes, it is going to cost.
If you have oil in there then it must be something else. Sometimes boilers go into "lock out" if there is a minor fault such as poor ignition, blocked jet, bad fan motor, It could be any of these, If you are renting - tell them there is no heat and you are freezing -it is their problem to sort out if they want you to pay rent. - Oh, and if it is not fixed soon you can withold rent payments. You can do that.
You don't measure heating oil in inches. Contact your landlord to find out what needs to be done.