As Vincenzo says, the correct translation of "Yo tengo sueno" into English is "I am tired" or "I am sleepy". Where Spanish uses the verb 'tener' plus a noun (sustantivo), English often uses a different construction : the verb 'be' plus an adjective.
The English sentence "I have to sleep" is different: this would be "Tengo que dormir" in Spanish. In this case, the two structures are parallel: a modal verb indicating necessity, plus an infinitive.