Returning player, feeling very lost =(

I played this game for about a month at release before RL took over. A friend of mine wanted me to come back and play with him so I did, but I'm feeling very lost on quests.

I leveled Archer at first to 15 then switched to Arcanist and I am level 13. I have no allowances left, and I can't find any quests to help me level =(

All I have in my journal is

Saw that one coming
Help me, Lord of the Dance
Call of the Sea
Leves of Aleport
Like Cats and Dogs

and a Levequest called
Tail in Tow

These are all 14-15 and I was wanting at least level 14 before doing them..

The beginning levels, especially on another class like you're doing, can be kinda funky.
I suggest completing what you can in your Hunting Log. You can also do FATEs to level fairly easily.

Thanks. I don't remember the Hunting Log..where can I find that?

And I'll start hunting down some fates to do.

Your Hunting Log will be in your menus. You do have it - it was given by your level 5 class quest on your initial class.

Hunting Log, a couple FATEs, and your class quests will get you levelled up in a class in no time, at least to the ~12-13 mark. Push to 15 through a bit more work with FATEs (each region has FATEs in that level range, though West La Noscea is the most commonly used) and you can start levelling in dungeons.

Levequest allowances also slowly regenerate over time - you regain 3 allowances every 6 hours to a maximum of 100. You can find out how long you have to wait til your next allowance under 'Timers' in the menu. :)

Also challenge log (unlocked in Limsa, somewhere on Hawker's Alley) help leveling up pretty fast. And do you daily roulette for guildhest :)