An experience essay can be written about an experience that is unique, but it doesn't have to be. Your experience and reaction will be interesting to the reader if it is something that they have not experienced, but it may actually be more interesting to them if they have also experienced something similar. It is important to think about that while you write. You might want to say things like:
"Many people may have experienced something similar.."
"My experience was unique to me, but other people may share this type of experience..." or
"What the experience meant to me was
Even though this is something other people may have experienced, I had never thought it would happen to me..."