I highly doubt there's a hole in the piston for one thing, especially if it went up after putting oil in the cylinder. The fact that it only went up 5psi after the oil when it was 35 before, suggests that your rings are not the problem. So, that leaves you with the head and headgasket(or block?).

How's your coolant look? If it doesn't look right, it could point to you having a headgasket problem, and pressure is escaping the cylinder and into the coolant passages.

Either way, the head will have to come off at this point I'd say, to see what the problem really is. From there you will be able to tell if it's a valve that's messed up, a headgasket, or whatever else it may be.

You can drive the car if you really need to, but it's not suggested of course. I wouldn't worry about damaging too much though, unless it is a headgasket and it's pumping pressure into your cooling system, your radiator and hoses might not like that much. I do think it'll be in the head though, so, yeah.