Legally, you only need a model release if you're using the images in a commercial manner - that is, displaying a person's likeness in a manner that implies that the person promotes or endorses your product or service. Note that simply displaying the image, or even selling the image (as art) is not necessarily commercial use. So, no, you don't need a release to enter the competition as a private individual.
However, the nice/polite/courteous(/ethical?) thing to do is to ask permission before displaying a picture of someone, such as putting it in a competition. Not legally necessary, but courteous.
Some people may THINK you need their release to use their image publicly. Even if they're legally incorrect, they might like to make a big mess of things if you use their likeness without prior permission. I generally err on the side of asking first, and getting a release, even if it's legally not necessary.
[EDIT] The above is mostly correct for the U.S. and may not be the same in other countries.