It depends on the size of the potato and on how much insulin you need per 10g of carbohydrate. Potatoes and rice both have fairly high carbs so you may need to weigh them to get an idea of how much is actually there...
I'm assuming you're on a combination of long acting insulin (basal) and short acting to go with meals (bolus). Most people calculate their bolus by adding in a correction dose (eg for me it's one unit of insulin for every 2 mmol/L that I'm above my desired reading) plus an amount to allow for the amount you're eating. The second amount is calculated by knowing (roughly) how much carb you're eating and then multiplying that by your insulin to carb ratio (which your clinic should help you with).
Can you ask your clinic about the DAPHNE course (I'm sure the UK diabetics will help if I've got the name wrong.)
The insulin to carb ratio varies drastically between different people (some people have over a 100 units per day, others less than 10), so you really need to ask your clinic about your insulin to carb ratio.
Good luck. Hypos are always horrid, hope you feel better soon.
ps Do you have a diabetic nurse at your clinic that you can ring for advice?