I am lvl 15 with my character and the best weapon I found so far is an axe of frost that does +10 extra frost damage (15 dam. + 10 frost). Shouldn't I have found anything better by now?

And my character is a sword based character so is there any good 1-handed swords to find out there?

Find the shrine of Meridia and do her quest. You will get a very nice 1-H sword as reward. I usually do that quest at around lvl 20 or so, not sure if there's a level requirement, plus it has a boss at the end. Just try it, I guess. lol

And I guess it depends on where you are looking. There are many different weapons around. At lvl 15 I guess you could find some Elven and/or Dwarven Swords, plus enchantments will vary.

25 points of damage really isnt that bad at level 15 problem with enchanted weapons at low levels is most likely your smithing skill is not high enough to improve them yet. At level 15 you are not going to find anything with much high damage +enchantment without really delving into a ruin or going after a wordwall and even then its all totally random.

most of them?

dawnbreaker, ghost sword, rueful axe, chillrend, nettlebane, trollsbane... not sure but maybe the ebony blade, I know it acts like a one hand but am not sure if it really is one, seems to me it was 2h

dawnbreaker is the meridia quest chain and the others I've seen and can't recall locations on

Lots. They are levelled and get better if you find them later in the game. Early on you can probably start on the ones you find now to start on your enchanting skill. Learn the enchants with the disenchant feature. Get some empty and filled soul gems to start upskilling Enchanting. If you are not interested in enchanting then Smithing ought to be looked at as a way to improve basic weapons. Smithing is probably more worthwhile early in the game than using those base level charmed weapons which lose their power anyway unless you have filled soul gems to recharge them. At lvl 44 I depend on my simple smithed steel and ebony swords which have much higher damage rating than the basic versions.

Rueful Axe is Clavicus Vile quest (It's not all that though, plus you have to kill the doggy for it -.-) lol
Nettlebane is a dagger and the quest starts in Whiterun, after you talk to the Danica Pure-Spring
Chillrend is obtain by doing the Thieves Guild quest, it's pretty far into the quest chain though
Ghostblade is obtained in Ansilvund

Also Ghostblade if you clear out Ansilvund.
Doing the Legion quests I got a couple of nice ebony swords from Tullius, though by that point I was able to enchant my own.

Be advised that intentionally crafting and improving items for the purpose of chasing higher skills to create the perfect weapon will drive your character level up before you know it, and you'll find that a good portion of your character's leveling life was spent at a forge or enchanting station rather than out actually adventuring. That was my experience, anyway. I'm on a second play-through to avoid that. Magic weapons of all types are randomly generated in merchant inventories and dungeons. Just keep looking (and having fun looking). Eventually you'll find something you really like.

As far as unique weapons that aren't randomly generated....

Spoiler:

The Shrine of Meridia is located near Solitude, and completing her quest will give you Dawnbreaker, an undead killing weapon that is also useful against vampires. The quest has a level requirement of 12.

My last character waited until mid 40s level to become thane of Riften and Solitude. The reward for both was a leveled sword, "Blade of Haafinger" for Solitude had a Paralyze enchantment, the "Blade of the Rift" had an Absorb Health enchantment. Both these weapons were very powerful at that level, useful for disenchanting if I'd not found both effects before.

at level 15 the weqapon that you have is pretty good.

if you want more damage... use the one handed perk tree.

25% more damage is the very first perk.