It should probably be important to note that one shouldn't use a offer as a way to demand a pay raise at his current employer. In most cases they'll tell you goodbye but in some cases a employer will try to counter offer someone leaving the company because they don't want to be stuck with finding a new employee. This counter offer will normally be a "promise" and should never be taken seriously. There's a high chance your employer wants to keep you in until they find a replacement then write you off. You fell for it unfortunately.
As always a counter offer should and ought to be in writing and in your hands. If you are "promised" a pay raise, then continue on with the process of leaving the company and securing a new position. Normally if an employer sees value in you, they will want to keep you on board by having a written counter offer in hand.
I'm not sure if this is your first professional job. If it is take it as a very valuable lesson. Now you may be out of a job with no offer in hand. Even if you are still employed you now have to rush to find a new job because you feel bitter and enraged at being ripped off. There's a high chance you will now take the first offer and ultimately repeat this mistake.
Whatever the case is don't feel depressed. Instead use it as a lesson and continue on with life. Nothing wrong with getting ripped off from time to time, just don't repeat it again.