Areas that need changes are in bold.
Over my past two summers, I have worked at Anisfield, a day camp at the JCC.
"Over the past two summers" doesn't sound very nice. Try saying "In the past two years during the summer months..."
"JCC" should be spelled out. You may know what JCC stands for but the reader does not.
For both years I was a counselor for incoming 1st and 2nd graders.
Use the words first and second instead of numbers.
I was assigned a group of kids
Assigned to a
group. Instead of saying kids, use children.
These kids were not only polite, but they also happened to be a pretty knowledgeable bunch of1st and 2nd graders
Again, instead of saying kids use children. Replace the numbers with first and second. "They happened to be a pretty knowledgeable bunch..." is to casual of a phrase. Try rewriting the sentence to say something like, "The children were not only polite, but they were also quite knowledgable for their age."
I got through that first summer with ease because the group of campers made it both easy to instruct and mentor them.
Using "the" instead of "that" would sound better.
The camper with anxiety problems and his mom
Mom is too casual. Replace it with "mother"
So, as we were walking to our second activity the child with anxiety issues realized that something was out of the ordinary, so being the 7 year old that he was, he broke down in tears
it would be a 10-15 minute breakdown
Write out ten to fifteen. Do not use numbers. You should write out any numbers that are below one hundred.
so being the 7 year old that he was
This whole phrase should be altered. To begin, write out the number seven. Instead of implying he is emotional because of his young age, try to explain that because the situation was undesirable to him it stressed his emotions.
"what do we have next?." or "where are we going?,"
Do not use double punctuation. Simply use the question marks.
Is that your entire essay? There was no real conclusion, you should insert a closing statement that sums up your entire experience.
Also, as a general comment, try to avoid using contractions. I noticed you used "wouldn't" quite often. Replace that with would not.
Hope this helps and good luck!