You might walk through the door at the other company, realise it’s a horrible place to work, and hand in your resignation at lunch time.
Do you not have any references at the company? Because that is the only way this could really happen. Personally I don’t blindly apply to a company without having any inside references.
Once you strong arm your employer to giving you a raise you’ve painted a big target on your back and you’ve announced that you’re willing to walk over money. It spells insecurity to them and the next thing you’ll find is the door hitting you on the way out.