Should I continue doing it? Is it dangerous if it goes into his throat and/or ears since the water doesn't flow out completely through the nostril?

It is possible that the solution only comes out of one nostril when using a Sinus Rinse, which may not necessarily indicate a problem. If your child's nose is very congested and the Sinus Rinse is not able to pass from one nostril to the other, it's a good idea to consult with your pharmacist for personalized advice on how to proceed.