To lie awake while dogs are baying through the night is a trial that wears upon both body and spirit, and your cry for rest is one the Lord hears.
You have asked that the Lord would silence the noise and give you sleep, and that He would guard you from the evil one through the blood of Jesus Christ. This is a right prayer, for sleep itself is the gift of God. We think we lay our heads upon our pillows and therefore we sleep, but it is not so. Not a man would close his eyes did not God put His fingers on His eyelids and send a soft and balmy influence over his frame to lull his thoughts into quiescence. So He giveth His beloved sleep, and when He gives it, none can take it away.
The Scripture speaks of enemies going round about the city like dogs that bay all night and rest not even at morning. David knew that sound, and what did he do. He said, My soul, wait thou only upon God, for my expectation is from Him. There is a rest which Christ gives at once to those who come to Him, a present rest, not rest after death only, but rest given there and then when we come to Jesus. He says, Come unto me, all ye that labour and are heavy laden, and I will give you rest. And there is also a rest which we find as we learn of Him and walk with Him, the rest of a learner who trusts and obeys. In this world we shall have tribulation and broken nights, for this is not our rest, it is polluted, we are passing through the desert to the Promised Land. Yet even here, believers do enter into rest, and in His service itself there is rest, as birds that sleep upon the wing.
Do not think that God is deaf to you, or that you must move His arm by a form of words. The deliverance we need from sin and from the pit was wrought when the Lamb was slain, and God has found a ransom. The blood of Jesus Christ is not a charm to be pleaded as an incantation, it is the precious price paid once for all by which we are redeemed from all iniquity and from the power of darkness. Trust in that finished work, and ward off the fiery darts of the enemy with the buckler of faith in what Christ has done. If there is an evil spirit at work, he flees not from a phrase but from Christ Himself dwelling in the heart by faith.
So I would pray for you in this way. O Lord God Almighty, Thou who seest Thy child by night as well as by day, give to this weary one the rest which Thou alone canst give. Calm the spirit though the noise continue, and in Thy mercy grant quietness without and peace within, that sleep may come as a gift from Thy dear hands. Cover this soul with the righteousness and blood of Thy Son, our only ransom, and let no fear nor power of darkness have dominion. Teach this heart to wait only upon Thee, to learn of Jesus who is meek and lowly, and so to find rest unto the soul. And whether Thou art pleased to silence the dogs or to give grace to rest through their barking, let Thy will be done, and let Thy beloved know that Thou keepest watch while they sleep. In the name of Jesus Christ our Lord, Amen.
Cast your care upon Him, and when you lie down, remember that He who neither slumbers nor sleeps is your keeper, and trust shall bring rest.