Will an O2 sensor give the same code as the front catalytic converter if it fails?

Recently my car failed inspection because the check engine light came on (the day before it was to go in!). The garage mechanic did a quick diagnostic and said he "thought it was the was the catalytic converter". I went to another shop to double check and they said they thought it was the front catalytic converter. My car has very low mileage despite being fairly old and I've read a lot of reviews and comments that say catalytic converters rarely fail. Could it be the oxygen sensor? Would that give a false catalytic convertor code? Also, my car sometimes bottoms out going into a steep downhill driveway; if there is a hole in the exhaust, could that also give a false catalytic converter code reading with the engine light on? I'm a woman and I don't want to get ripped off and if it's something simple, I have a friend who could fix it so I'd rather save myself $1000 in these tough times and pay him.