Yeah, Storm Coast and Forbidden Oasis are good spots to level up a bit. You shouldn't need more than another level. (Don't go inside the temple in the Forbidden Oasis, though. That's for higher levels.)
For In Your Heart Shall Burn, I'm guessing the part you have trouble with is with the last trebuchet, after you leave the Chantry. There is a supply cache right there, but I assume you're using it and still having trouble. Since you're gonna restart the quest anyway after leveling up, some tips:
The fights on the way from the Chantry to the trebuchet will be easier if you leave the supply caches inside Haven alone during the first part of the quest. You get a full party heal and health potion refill after the cutscene at the Chantry. You can also skip the fights on the way to the trebuchet by using a Rogue with Stealth.
Since you're fighting the Red Templars, focus on the Marksmen first, as they can do the most damage. Knights and Horrors next, then Guardsmen, and vanilla Red Templars last. I don't recall fighting any Shadows during this quest, but if I'm wrong, put them on the same level as Knights and Horrors.
The basic plan is to crank the trebuchet until you can't anymore, then kill the bad guys, then repeat. You can and usually should keep cranking even once bad guys start to appear; let your companions handle them until you're done, then join the fray. Once the last enemy is dead, go back to cranking. The last wave of enemies includes Knight-Captain Denam as a behemoth; you don't actually have to kill him (or finish the wave) to start the last round of cranking. If your defense is high enough, it might be better to just finish the trebuchet. I would also take out the Marksmen in the last wave before tackling Denam; those guys are assholes.
I find Cassandra makes a good tank for this part; Blackwall is cromulent, too. I usually bring along a mage with Barrier as well; you can have them cast it on you while you're cranking. You don't really need a rogue on this quest unless you want to Stealth past some fights, so if you want to bring two tanks or two mages, go for it.
For warriors, keeping Guard up should be the #1 priority. This goes for companions as well; you can set guard-enhancing abilities as preferred on the Behaviors menu. Mages should have Barrier as preferred as well. As a mage or an archer rogue, try to keep out of the melee as much as possible (Leaping Shot is very helpful with this for archers). Stay close to the trebuchet, ideally between it and the supply cache (which you should wait to use until you're down to 1 or 2 potions). Bringing along some Regeneration Potions or Rock Armor Tonics is not a bad idea, either.
Crafting yourself some gear with the best schematics and materials you've found so far is not a bad idea. There are some decent Tier 2 schematics for sale in Val Royeaux and at the Black Emporium, or maybe you've found some already.
Good news is, the rest of the quest is basically cutscenes. Enjoy Skyhold.