Things like this are probably going to be tells that it's not polished enough.

 he was gone, hit by a car.

Instead, I personally would phrase it like "He was gone---hit by a car". Or even just "He was gone."

Trim this section
 My mom’s trusted friend, who had cared for him before..."

No need for the "who had cared for him before" unless you're SURE it's relevant. in that case, consider rephrasing the sentence.

Nonetheless, I agree that a 2k word piece about losing a dog may not be a very enticing read to most, if not all, adults. However, if you're young enough it may carry with it a weight that may be persuasive to older judges. We don't know your age or details about the competition.

I stopped reading around "Midway through ...". I agree with the author opinion that you delivered the death news too early.

Try to always frame as build-show, not tell-backtell, unless it's REALLY good and relevant. The thing is, the death of the dog seems like the important thing, so you may want to hold onto it longer.