Thank you for your question.
I am Dr. Su S. and I will try my best to help you.
A little aspiration of water can happen during bath.
It should not cause secondary drowning effect.
Viral infection, cold allergy can be a factor.
But labored or shallow breathing can be due to bronchospasm.
You have switched on humidifier.
In mild case, it can help.
In bronchospasm she can need bronchodilator and other medicine as nebulizer.
I would suggest to take her to hospital for an evaluation and management.
I hope this information will be helpful.
If you have any query, please feel free to ask.
If you are happy with my answer please click on the Excellent/Good rating.
Wish her healthy life.