1. Practice getting hit. (Preferably with a partner who has enough knowledge and skill to avoid injuring you.)
2. You can practice at low risk of being seriously injured. Again, you need a partner who is sufficiently knowledgeable and skilled to help you without hurting you.
Grappling arts that emphasize groundfighting give you more practical experience of fighting usefully with lower risk of injury. Because you more often start out on the ground, you're much less likely to be injured in a fall. Because you strike less, you're less likely to injure yourself either by striking something or by being struck.
If you want to get past the non-useful reactions to being struck, though, then you probably also want to do some striking artor sport with contact--boxing, kickboxing, muay thai, et. al. Just be sure to use safety equipment and work with someone who has both skill and empathy.