Yes, it can cause harm. Do not drink any more.
Get emergency help immediately if you have mouth/throat burning, repeated vomiting, drooling, trouble swallowing, chest or abdominal pain, coughing/choking, difficulty breathing, confusion, or if it was a concentrated/industrial product. Household bleach is often dilute and small accidental swallows may cause irritation, but concentrated products can cause serious burns.
Poison Control guidance
If this was intentional or you feel at risk of drinking more, please call emergency services or a crisis line now and move away from the product.