Am doing something wrong because every enemy seems so much stronger than me and with no real way to level up
What's worked for me, as a fairly new player who had the same problem:
As was said above, the primary way to gain XP is through quests. Enemies don't grant XP. Which basically means avoiding combat unless it's intentional or can't be helped.
Study in the evenings (books in Krowly's bedroom) to learn some new spells. Three spells of special note are Fireball, Freezing, and Thunder. What the game doesn't tell you (unless I just missed it) is that these spells level up with use. For example after 50 uses, Fireball becomes Fireball+, and after 50 more uses it becomes Fireball++. So after learning any of these spells I would just run around the woods outside of town everyday and spam them on Slimes until I ran out of MP. Sleep is also very useful on large groups.
Then every now and then you will come across a problematic mini-boss that you may need to look up in the guide. The Busty Elf (who's not even a mini-boss) gave me so much trouble at first. But now I'm practically one-shotting them.
Plus there are just certain areas that you can but shouldn't go to while low level.
I basically focus on quests, learning and leveling new spells, and grinding out Gardening, Cooking, and Alchemy before I even start really working on relationships and stuff.