I have noticed that many authors incorporate the use of fragments and comma splices in their novels. Given that this is acceptable practice in a novel, is it acceptable to use a comma splice or a fragment in a short story written for English class?
In general, No!
Your papers for English class should follow the rules of English grammar including proper punctuation. What you do as a novelist later in life is your own affair.
If the purpose of your paper is to demonstrate a particular affect achieved by bending or breaking certain rules it may be acceptable; but you must first demonstrate competence at using the language in the proper way. In many cases such rule bending is a prop used to hold up prose so broken they couldn't be sustained using normal rules. If you learn to communicate well inside the boundaries of established grammar rules, when you do choose to break them the result will be even more efficacious.
You can assume that published novelists know how to construct correct sentences. If they chose therefore to include a fragment or, less commonly, a comma splice, they probably were aiming at a certain effect. You could analyse the examples you find to determine what that effect might be and if you would like to achieve a similar effect in own fiction writing.
Of course, while still writing for grading by your teacher, you should first check that he or she has no objections to such usage.
Acceptable to whom? When I see glaring grammatical errors in a novel it feels unprofessional to me. If you can state something in a way that is grammatically correct, that does not change the meaning, feeling, or intent of the line then do it correctly.
As an artist you can take licence, but it should add some meaning that is not evident or conveyed otherwise. As a general rule unless breaking the rules adds to art, it takes away from it. If someone reads the work and there is any doubt that the sentence was not an error then it is an error.
I think there's a general tendency to use less punctuation latterly, and this inevitably leads to more disconnected fragments and "comma splice" constructions.
By implication, an increasing number of such usages are likely to be considered unjustified. I think the purpose of punctuation is to clarify meaning and aid legibility, but often the primary target of criticism over "incorrect" punctuation is simply the failure to follow "rules and norms".
It's often said that "established" writers can get away with breaking the rules more often, and I personally don't see this as a problem. But I do think those who are still learning the rules should by default tend to stick to them. And as ever in an educational context, the default should definitely be to learn and apply the rules set out by the teacher, not just assume "anything goes".
TL;DR: Not wishing to be snide - OP asked whether such deviations from standard usage are okay in a short story written for English class. Possibly just a typo, but I take this as evidence he is not yet ready to experiment with creative rule-breaking.