Can small amount of Vaseline in nostril (to treat dry nose/nose bleeds) cause immediate post nasal drip and hence coughing?

Not typical. That is not a typical response but not worrisome if that is occurring. You may also try a nasal gel like ChitoRhino Nasal gel for a dry, crusting nose.

Related Questions

Pea sized amount of vaseline 1-2x daily good idea to help nostril recover from dry air which was causing nosebleeds? How far up the nose to lube?

Yes vaseline is good. It is very useful to apply Vaseline to the dry skin. In the nose areas you can apply it with your finger tip which can go up the nostrils for about 1/2 inch before it becomes uncomfortable, then you stop right there and gently rub it to spread the moisture around.. Read more...