I have had countless prayers answered by praying the exact way you are which lets me clearly know that God is listening to those prayers. Although I have been searching the scriptures trying to find a verse to back that up, and I have not found a scripture that clearly discusses not praying aloud. There are a few scriptures I'll let you read over and let you get what you can out of them. Heb 4:12 For the word of God is quick, and powerful, and sharper than any twoedged sword, piercing even to the dividing asunder of soul and spirit, and of the joints and marrow, and is a discerner of the thoughts and intents of the heart.
Ps 55:17 Evening, and morning, and at noon, will I pray, and cry aloud: and he shall hear my voice.
Both of these scriptures seem to say that it would be alright to pray aloud or in you heart. The important thing is to mean what you pray. Remember Christ actually sweat blood when He prayed. Also remember the outline prayer of how to pray. In Matthew 6:9 Jesus tells us to pray in this MANNER. In verse 7 He tells us not to pray in vain repetitions. Repetitious prayer are not from the heart. God wants you to walk with Him in order to have a close relationship with Him and COMPLETELY depend on God.