I woke with a dry cough and sleep in my eye. could this be a bacterial infection? both my kids are also showing some sleep in their eyes and cough.

Anything possible: But more likely to be a viral uri. See a doctor if there is fever, changes in respirations or difficulty breathing, or any disturbing symptoms. Hope you are all better soon.

Likely viral: I would bet viral infection. Spreads through the family by co contamination ( hands to face, mouth, nose) ;/or cough particles inhaled. Infectious process develops over several days then gradually resolves 2 to 4 weeks. Take proper precautions to avoid spreading to eyes and others. Take usual symptom relievers like tylenol, (acetaminophen) decongestants, cough suppressants, etc. Keep well hydrated and get sleep.