First of all, what you have done is create a comma splice. In other words, you are using commas between independent clauses.
Most of the time, this is considered to be an error (unless a coordinating conjunction is used); however, comma splices can be used for deliberate dramatic effect. Most often, this occurs when the clauses are short.
Below is an Associated Press question and answer on this subject. I have removed the bold formatting that the source uses, and added my own emphasis to part of the answer.
Question:
Is this an acceptable comma splice?
He said, “Winning isn’t everything, it’s the only thing.”
And:
"Many of you have jobs, many of you have families," Sen. Al Franken told Virginia Democratic leaders. (Comma OK?)
Isn’t it inadvisable to use semicolons in quoted dialogue? Could a dash work in place of the comma, too?
Thank you!
Answer:
Interesting. Yes, both of those are comma splices and yet both seem OK. I think maybe it's a reflection of the written version mimicking the spoken version in cadence. Also, there are arguments that short clauses are OK when comma-spliced: He came, he saw, he conquered. To be safe, a period or dash would accomplish pretty much the same thing and would be absolutely correct. A semicolon would be jarring.
Per Wikipedia:
In English grammar, a comma splice or comma fault is the use of a comma to join two independent clauses. For example:
It is nearly half past five, we cannot reach town before dark.
The comma splice is sometimes used in literary writing to convey a particular mood of informality. Otherwise, it is usually considered an error in English writing style. Some authorities on English usage consider comma splices appropriate in limited situations, such as informal writing or with short similar phrases.
Finally, in this article, Texas State University mentions some exceptions to the prohibition on comma splices:
EXCEPTIONS: If you are in doubt of the correct punctuation, use the more traditional methods.
A comma splice is permissible in a series of independent clauses (three or more) where the last two clauses are separated by “and, but,” or “or.”
The Yo-Yo King demonstrated his new trick, the Skateboard Princess
performed her new stunt, and the manager of Play Palace treated
everyone to chili dogs and root beer.
Achieve a dramatic effect by using commas without coordinating conjunctions to link several brief, closely related independent clauses:
He came, he saw, he conquered.
A comma may be used to separate a second clause which reverses a negative first clause:
That night the princess did not sleep, she danced the night away.
So, you may still claim dramatic license for your use of a comma splice—even if yours seems to have clauses a bit longer than the examples given as acceptable exceptions. Whether you should, or whether you should rephrase your passage, is up to you.