In my opinion, too many of your sentences start with "I <verb>", so you might want to rephrase those.
creating art relating
"Art that was related" sounds a bit better
I felt very accomplished because of the amount of depth these pieces had as a result of this influence.
The first part could easily be gotten rid of. "As a result of this influence, my work gained a significant amount of depth" or something like that.
I put more effort into my work because it truly meant something to me and the art conveyed a message.
Same here. "My work truly meant something to me and conveyed an important message".
I realized that I can use my skill to make an aesthetically pleasing piece that draws the viewer in. Watching them take meaning and emotions of the piece away was invigorating. I learned I can use my art to influence my viewers thought and hopefully invoke changes in their behavior and thought.
I would rephrase it to show that you use your artistic skill to make sure your message made an impact on viewers.
Also, some of your sentences just do not connect smoothly into a text that is pleasant to read.
I believe that I am a strong candidate for the School of the Art Institute of Chicago (SAIC) undergraduate program because I am energized to take my creativeness to the next level. I am ready for the immense work load and time investment that a school like SAIC requires. I have always gone the extra mile in both my academics and artistic endeavors.
I would put it like "..because I am ready to take my creativeness to the next level, which would require hard work and time investment. Always going the extra mile in <..> has taught me not to be afraid of challenges".
I spent three weeks this past summer in the college atmosphere creating many new projects.
Projects related to what? Did you continue to convey the message which you mentioned earlier?
I am excited about having the Art Institute of Chicago as a resource. This museum and all its collections and resources will be an added bonus.
One medium-length sentence is better than two short ones, from what I believe, even though I might be wrong.
I will bring a thoughtful and creative passion to the school. I will continue to explore societal and environmental issue and incorporate them into my artwork using it as a tool to evoke change. I will use all the resource provided by SAIC to expand my knowledge and develop a career path that will lead to a successful career.
"I will add to the community of thoughtful and creative students as I wish to continue to explore <...> issueS <..>." Also, "resourceS" and "career path - career".
Give it to more people to read! I may not be the best source of information of how to write amazing and thoughtful essays. Check for repetitive phrases and words, get rid of the I's at the beginning of every sentence, also avoid many short sentences in a row as they tend to stop the smooth flow of text, making the reader pause mentally at every period.