You have inadvertently taken a more stylized approach to your writing that your teacher is not comfortable with. You are, apparently without being aware of it, using one or more forms of ellipsis in your example. An ellipsis is the omission of words "necessary for a complete syntactical construction but not necessary for understanding".
Your sentence might be more syntactically complete with the added words highlighted below:
As I returned to my seat, my heart was still racing, and other kids started to talk to me.
The omission of the "and" it called asyndeton, which is a case of one or more conjunctions being omitted from an otherwise complete syntactical construction. Asyndeton is a specific type of ellipsis. (I'm not certain if there is a special word for the ellipsis where "was" is omitted, but it is still an ellipsis.)
Alternatively, your example might be more complete like this:
As I returned to my seat, with my heart still racing, other kids started to talk to me.
In summary, you can (and you did) leave out the highlighted words above and still have a perfectly understandable sentence.
You teacher is, no doubt, focusing on "complete syntactical construction" and expecting you to demonstrate that you understand how to write that way. However, it is not necessary in common practice and you will see it used frequently as part of a writer's style.
One other point I would like to make is about the writing form known as "stream of consciousness" or narrative mode. As the reference states, this "interior monologue" represents (or can be understood to represent) mental thoughts captured directly into writing. Specifically:
Stream-of-consciousness writing is usually regarded as a special form of interior monologue and is characterized by associative leaps in thought and lack of punctuation.
So this narrative mode takes license by compacting the sentences as they might actually be perceived in the mind of the narrator. It tends to humanize the writing, and can have a strong effect in capturing the readers' attention.