exp not increasing at all level stuck

[Enkidoh]

I suspect that wasn't actually EXP you were rewarded but an increase to the amount of Grand Company Seals you can hold (hence why your EXP level did not increase) - GC Seals are a currency you get for doing Company tasks like supply missions and which you can spend at your GC HQ for items and gear. The amount of Company Seals you currently hold can be found under the Currency tab of the main menu.

If a quest or supply mission rewards EXP it will usually have a distinctive gold hexagonal symbol beside it, where as GC seals are a document icon.

The other thing I can think of is when you supply items to Supply Missions it actually gives you EXP not towards battle classes, but only crafting and gathering classes like Carpenter or Blacksmith, based on the item you supply. You do not have to currently be set as that class to gain EXP towards it though a Supply Mission, which in hindsight I think might be actually what has happened.

Open up your Character screen and check the Classes and Jobs tab, chances are you now have levelled up in one of the Disciples of the Hand (crafting) or Disciples of the Land (gathering) classes as a result.

Either way, welcome to Eorzea!