Submitting paper to arXiv as an undergrad
I will leave the question of whether or not you should submit the paper to arXiv versus another venue for discussion elsewhere. However, I do agree with the comment that you should talk with the professor who gave you the assignment about your plans, as he or she may have constructive criticism for you.

In general, if your work represents an original contribution, and you feel comfortable with sharing it with the public, then yes, you can go ahead and submit it to arXiv. You should note, however, that in a number of fields, papers cannot be submitted until you have been endorsed—that is, recognized as a valid submitter by someone who has already themselves submitted a number of papers in that area. If the professor of the course is someone who can endorse you, then that should be sufficient.