Is what I mentioned considered a vow even though I didn't win the competition, and is it possible for a vow not to be fulfilled, and why? And are there specific words for someone who wishes to make a vow?

What you said is considered a conditional vow (nadhr mu'allaq), which is disliked (makrooh). It is not obligatory to fulfill it unless the condition upon which it was suspended is met. So, if you do not win the prize, you are not obligated to fulfill it. A vow may not be fulfilled due to a wisdom Allah wills, and it is valid with any words that indicate commitment to it.