Make sure you have fully cured the barrel before trying to use the barrel wax on your leakage. Your barrel normally will soak in the liquid which will cause the wood to swell against the hoops then it seals itselft most of the time. After you have fully cured the barrel and you still have some stubborn leaks then give your barrel wax a try. Barrel wax is very easy to use. First dry the barrel as best you can with a dry cloth. Then put the leaking side of the barrel on top so there is not active dripping while you apply the wax. Get a dab on your finger and press the wax in to the barrel area that was leaking. Wipe away the excess wax and try to cover any surrounding areas. No need to stack in on thick or anything. You should be able to wipe off the excess and the wax you pressed in to the wood grain should be enough to seal it up.
Video – How to use your barrel wax to seal the oak barrel