Breaking with a punch is always risky. When kicking, you strike with large, relatively flat bones that are covered with thick skin and have some padding beneath the skin. A knife hand strike also uses the large, flat, padded part of the hand. However, a punch strikes with the knuckles, which are pointed bones with no padding, unless you have built up calluses on over the knuckles such as Oyama, the founder of Kyokushinkai and great power breaker, did on his hands. In his later years, Oyama said he regretted the damage he had done to his knuckles.
If you can use you hand without pain, then probably nothing is broken. Sometimes, the nerves that run between the knuckles get bruised and take time to heal. I used to have no pain after a punch break, but afterwards, when I stuck my hand into my pants pocket, the seam of the pocket would rub the nerve between the first two knuckles and cause a sharp pain. It sometimes took months for the hand to heal. Most of the time, the pain after a punch break is caused by a “bone bruise,” where there is a contusion on the bone. A bone break usually takes 6-8 weeks to heal, but a bone bruise may months or years to heal before it is not a problem.
Some of the Chinese martial arts use ointments, crèmes, etc. that are supposed to toughen the skin. Okinawan karate styles use various types of forging to toughen the hand and build calluses on the knuckles. Unless you are dedicated to breaking, it is not work the chance of injury to break more than two boards with a punch,