I've had this problem before, both due to medication side effects, and due to spiritual problems...it's not necessarily demons, but it well could be.
I like that particular psalm for this application. The line, "You prepare a table before me, in the presence of my enemy"
God is so faithful, he doesn't just want us to beat the enemy, he wants us to be so trusting in His grace and protection that we don't need to beat the enemy, we are freed from his power against us by the blood of Christ. Sometimes we forget that though and the enemy will come in and scare you if he can get away with it.
Danschance has some good ideas about forbidding demons in your room in Jesus name, sleeping with a Bible. I haven't read the book but it sounds good....there's an important thing to note when dealing with demons....it is prayer in faith and obedience that sends them packing. Even a non-believer can summon some confidence and tell a demon firmly that it's not welcome and it will oft times leave, I have seen this happen. It is your faith that it can't hurt you, that protects you.
This is big-- do not do any of the following as they are anamistic/thelemic practices that are at best superstition and sometimes border on witchcraft.
Do not anoint your room with oil. If a priest wants to do that, fine, they are trained in ritual magik, you're not.
Do not burn incense in an attempt to deter demonic activity. Our prayers are the incense.
Do not sleep with a miraculous medal, or other blessed object, or good luck charm. If you need something tangible, the Bible is good to sleep with, you can leave it open if it helps your faith, but remember, it is faith that does it.
They can only hurt you if you let them. If your prayers aren't doing it, it might be that at this point your fear is inhibiting your faith, in which case you should repent, and you should ask someone to pray for you and over you and your room. Talk to your parents or pastor, and get a check-up with your doctor as medical things can cause similar problems.
Don't fear. It might be scary, but it can't hurt you. Perfect love casts out fear, which takes the weapon from the enemy.
There's an account (I don't know how true it is, but it helped me) of Martin Luther waking up kinda startled, and seeing the enemy next to him in bed he said, "oh, it's just satan" and rolled over and went back to sleep. Even if it's made up, that confidence works, I've tried it. I've had some spiritual warfare in my day, and nightmares, pm me anytime if you wanna chat.
Also think of this, people are reading this and already praying for you, so you may see some improvement already! =)