Yes, raising the hands is an established etiquette of dua and a cause for it being answered. The Prophet (peace be upon him) said, "Indeed your Lord is Modest and Generous; He is shy to return the hands of His servant empty when he raises them to Him," so extending the hands with the palms facing up is recommended for general supplication. Allah also commands us to call upon Him with humility: "Call upon your Lord in humility and privately" (7:55). Note, however, that some du'as tied to specific occasions (such as during the khutbah or the tashahhud) were not accompanied by raising the hands, so we follow the Prophet's practice in each context.
Informational, not a personal fatwa. Consult a qualified scholar for rulings on your situation.