Can papillae become raised on tongue from blocked nose and breathing through your mouth?

Dry mouth: If you are breathing through your mouth versus through your nose due to blockage, it is possible to inflame the papillae, causing them to be raised.

Tongue papillae: Can be affected by lots of things including what you mentioned. Dry tongue, allergies, medications, smoking, poor oral hygiene are just some of the more common ones. Suggest you use a tongue scraper on a daily basis as part of your daily oral hygiene routine and keep hydrated by drinking enough water throughout the day (which is good advice for everyone).