...
"You...are from God and have overcome them because greater is He who is
in you than he who is of this world."  I John 4:4
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It's good that you prayed....prayer cover is very important.  About their 
"power"....it is not awesome power and it can be rebuked in Jesus' name
and made to be no power at all.  Again, you did the right thing by praying.  
Pray always.
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Yes...this is definitely Spiritual Warfare.  Spiritual Warfare is a topic
I have looked a lot into.  Even our struggles with daily sin involve the
constant Spiritual Warfare.  There is a constant war in the spiritual
realms and it taps into us as our spirit wars with our flesh.  I have
literally felt the war within me in the past.  We cannot take this lightly
....wow we gotta pray.
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"Submit yourselves, then, to God.  Resist the devil and he will flee from
you." --James 4:7

1.  SUBMIT YOURSELF TO GOD
First thing to do is pray.  Pray for God's guidance and protection.  Get
into His Word.  I will give you some verses here:
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Satan always loads his flaming arrows and stoops and attacks, but with
faith in Christ, the arrows are reflected.  Whitecross, a Christian metal
band, sings in a song called "If He Goes Before Me" the following:  "I
know your eyes see me as being weak / And without any strength or wisdom
to call my own / I know the odds they don't favor me / But my friend have
you forgotten I'm not alone / The Father's here with me / Already fighting
the battles I can't see / If He goes before me / How could I ever lose /
If He goes before me / Before I ever begin / I know I'll win / If He goes
before me."  Cling to the message of those lyrics.  Believe them.  Know
that Christ is out in front of the front lines of the saints fighting
battles we don't even see.  Then by His Grace our faith grows....our
faith is our shield.

2.  RESIST AND REBUKE THE DEVIL AND he WILL FLEE FROM YOU.

Demons hate scripture...but especially the scripture where Jesus gives
us authority to rebuke evil spirits.  Remember that in Ephesians 6:17,
the Word of God is the Sword of the Spirit.  

"He [Jesus] replied, 'I saw Satan fall like lightning from heaven.  I
have given you authoirity to trample on snakes and scorpions and to
overcome all the power of the enemy; nothing will harm you.  However,
do not rejoice that the spirits submit to you, but rejoice that your
names are written in heaven.'" --Luke 10:18-20
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I know that this world looks at us as freaks when we bring up things
about our faith especially dealing with Spiritual Warfare, but our home
is not here.  We are aliens and strangers.  Our citizenship is in Heaven
(like Luke 10:20 states above).  Jesus even said, "My Kingdom is not of
this world." (John 18:36).  Perhaps God is allowing you to be stretched
and tested, but remember "No temptation has seized you except what is
common to man.  And God is faithful; He will not let you be tempted
beyond what you can bear.  But when you are tempted, He will also provide
a way out so that you can stand up under it." (I Corinthians 10:13) AND
"We are hard pressed on every side, but not crushed; perplexed, but not
in despair; persecuted, but not abandoned, struck down, but not
destroyed."  (II Corinthians 4:8-9).  When attacked, pray...."Father God,
the attacks come my way, but I know that you protect me.  Father, I pray
against these attacks and the attackers.  By the authority that you give
to me, Jesus, I rebuke this evil in your name Lord Jesus and I command
this evil to flee from me in the name of Jesus.  Father, please deliver
and protect your people from all evil, hindrance, and harm."

Rely, Rebuke, Resist....

You may need to pray over and over relying on God, rebuking the attack,
and resisting the devil.  The enemy will flee, but he won't go far.
Jesus tells us that often an evil spirit will return with additional
evil spirits, but you and I know that there is power in Jesus' name...
that at His name every tongue will confess and every knee shall bow...
even those of demons.  The demons believe in God and shudder (James 2:19).  
...   
There is a prayer in the air for you.  While the devil and his legions
fire rounds of fiery darts of temptation, the saints hold up their
shields of faith, fire rounds of prayer, and in the meantime, the Father
goes before us fighting battles we cannot see or cannot even comprehend.  

		       "What's in a name 
			that the demons flee?
			What's in a name 
			that the captives go free?
			What's in a name
			that every knee shall bow?
			In the name of Jesus,
			Name above all names,
			There is power and glory
			Forever and ever,
			Forever and ever."
					--Bob Hartman (Petra)
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The Father is with you ... in these battles.  And when the devil attacks, 
remind him of his future (Revelation 20:10).  Nothing can separate us
from the love of God through Jesus Christ (Read Romans 8:35-39).  Hope
this helps....oh, and in these crazy times, give God praise.  

			In Christ,
			  Jamie
                        the Beacon Deacon