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If the bed were a few inches higher, I would be able to store my suitcase beneath it. Is there anyway to raise it and still be able to support a person lying down?
I may be looking for something like this though $20 seems a bit much for something that gives a few more inches and I'm in Canada. I've heard of using milk crates but wouldn't they break? If not, where would I get them from?
The bed has wheels and is for a single person.
Go to your local hardware store and buy 4 of these. Maybe $1.50 each?
Bring them home, and lay them on their side.
$6 and you have a very sturdy 8" lift.
If you need higher, buy 4 more.
If it is too heavy for you, pay a youngster $10 to haul them up the stairs. Still under $20.
Go get yourself an 8' untreated 4x4 (~$10.00).
Determine how much higher you'd like the bed to be, then cut the 4x4 in appropriate lengths adding an inch to each length.
For example:
If you want the bed to be 4" higher, cut the 4x4 in 5" lengths.
using a spade or Forstner bit of appropriate size (just slightly larger than the bed frames feet, so the feet will fit into the hole), bore a hole to the depth of one inch.
place the frame on the 4x4 pieces, such that the feet of the frame sit in the holes you bored.
NOTES:
Make sure you use untreated wood. Pressure treated wood may damage, and/or stain your bed frame and flooring.
I'm assuming you have a drill press and the appropriate bits, so the cost of the project only includes the lumber.
Making the leg extensions too high could cause the bed to be unstable, leading to property damage, injury, and or death.
The best way to raise your bed is too use a product designed for the task. These bed risers from The Sleep Shop will do the trick. They're going to raise your bed about three inches but keep the sturdiness so there's no rocking! 
They aren't the prettiest things but, they'll work!
We use a set of those lifters you linked for our king-size bed. They work great. I would NOT use milk crates, as their open frame isn't designed for point-weight support like a bed frame foot.
If you're looking for a low-cost lift of a couple inches, a small piece of lumber (4" length of 2x4, for example) would work fine. Be aware, most basic bed frames have wheels, and can roll off blocks of wood. This can be a bit shocking, as it's likely to happen when you're moving on/off the bed. One advantage of the $20 lifters is they have a lip which traps the wheel. They also interlock, so if you need to lift the bed a bit higher (2 lifters worth) it's still shear safe.
Whatever you place under the feet of the bed, make sure you raise ALL of the bed feet the same distance. Larger beds (kings, some queens) have supports in the middle of the bed as well as corner supports; they must all be lifted equally. Other than that, anything which will support the weight without collapsing will work.
(postnote) The above applies to basic angle-brace steel frames. More sophisticated/expensive frames which incorporated head or foot boards or other features may not be liftable this way. Well... the basic idea of "lift ALL the feet equally" should still apply, but you may have to do something to also lift the header/footer. These concerns will be much more frame specific, and we'd need more information (pictures?) to properly answer.
First you need a base. I suggest you go to the local hardware store and get the thickest piece of plywood. You need something that is the same size of your bed but rigid - actually have them cut it about 2 inches short lengthwise and widthwise so that the board is hidden on each side. Bonus - look on craigslist for old bed frames being throw out, wood, old tables or whatever. You have to look for stuff in your area and use your imagination a little. You might need a circular saw (or beg the person throwing out the wood to cut whatever for you). This could be free or $12 for the plywood at big box.
Then I would use milk crates. How many you need depends on how stable you want your bed to be and how big your bed is. A basic twin with a board under it can definitely be held by just 4. You could add a couple in the middle and go 3 on each side if you want extra reinforcement. You can get these for free at some recycling centers or supermarkets.
Myself I had a rig like this in college but used textbooks instead of milk crates.
