A 3/4 inch wrench fits the bolt head.What is the actual size of the axle?
The size of the nut has nothing to do with the size of the axle. My guess is that you have 14mm axles since 3/8 axles usually use 15mm (about 5/8) nuts. Unless your bike is REALLY old, like from the early 80s or earlier you bike has METRIC nuts and you should use only METRIC tools.
Get a ruler and measure it.