For migraines, most doctors recommend an MRI over CT scans since it gets a little more detail, but either should be helpful in ruling out anything major. I was disappointed I got the MRI recommended to me, because it costs more, takes longer, etc! Luckily I found an open MRI place so I won't be claustrophobic
and with insurance, at least it's just my deductible of $500.
For a peace of mind, tumors RARELY are the cause of migraines. And a ruptured aneurysm would mean that you probably wouldn't make it and still be here if you had one. I felt worried at first when my migraines were getting worse, but since I have them regularly, I know it isn't something life-threatening.
Unfortunately there are SO many things that can cause them. A neurologist or other doctor that works with migraines can help you figure out those causes and how to prevent them and treat them. I've heard of some people who get them after sleeping!
I also get very tired and have a TON of mental fog, so I understand how frustrating that is. I often feel like it's a bad idea for me to drive to work in the mornings because I feel drunk. I also struggle at work with being able to concentrate when I feel like I'll fall asleep. I think I'm the type that needs good sleep and naps. I get 6-7 hours a night and think I need 8-9. It's amazing what sleep deprivation and stress can do to your body. Migraines can also get you in that mental fog, even if you don't have the pain going on.
Definitely look into seeing a doctor so you can get it under control! Migraines are miserable and you don't want to have to go through them if you can stop them. They can also talk to you about the falling asleep thing. Do you ever feel well rested after waking up? I'd be curious if you had a sleep disorder, like narcolepsy. I always thought a person with that would randomly fall asleep even while walking, etc, but it's often not like that at all. It's worth at least reading about to see if it's a possibility.
I've also heard that some medications can cause this. I noticed that Prozac made me feel this way. At first it was very relaxing and I felt great, but later on, it became very frustrating because I felt like I was stuck in a cloud and couldn't snap out of it. Same thing when I have sinus and ear problems from allergies. The vertigo drives me nuts! I take birth control and some people say that makes them feel a lot of brain fog, but I'm not sure!
EDIT: Oops Tingles, I see that you mentioned both the CT scan and MRI. Maybe that's why they do the CT scan first- so it's a little easier and cheaper. They recommended I go straight to the MRI. I have mine scheduled in about a month.