Try keeping mouth open and breathe through the mouth. The trick is to not tilt your head too much, but to tilt the neti pot so that water flows with force. If the neti pot is fully covered by one of the nostrils and your head is reasonably tilted and you breathe thru the mouth, water will definitely go inside one of the nostril. If the water flow is properly regulated by tilting the pot, there will be enough water and breathing thru the mouth, you can ensure continuous flow.
If water enters throat or ear, it means you're tilting your head too much.