breaks can be both a transitive and an intransitive verb.
A stone broke the window.
"Window" is the direct object.
A pane of glass breaks when struck sharply with a hard object.
If you say "My hand breaks" without a direct object, your hand becomes analogous to the "pane of glass" in the second sentence, the example of the intransitive use. That is probably not what you mean to say. You probably mean to say that at this moment, your hand is injured. Your hand is broken.
Broken is the past participle of the verb break used adjectivally.
To express that something is currently in a particular state, we use "is" plus the past participle:
The glass is shattered.
The chair is painted.
The table is varnished.
The potato is peeled.
The past participle of many verbs is formed by adding -ed to the verb's bare infinitive:
But some verbs are irregular and their past participles are formed in another way. For example