Is it possible to to mess up a character build in Dark Souls?

I just barely beat the two gargoyles in Dark Souls. I'm using the Zweihander sword I found in firelink shrine and for that I needed to get STR to 24. I like the idea of playing a STR-heavy character, but a couple of very painful encounters with dark phantoms made me wonder if I should be investing more into health or stamina or dexterity or whatnot.

I don't really want to read a guide that really lays it out because I want a pure experience - but is it possible to completely mess up a character (especially for New Game + ) by going all out on HP + str and completely ignoring defense or dex?

If you're talking about a strict PvE build for your character, it's not that you'll mess up a build. You'll more likely paint yourself into a corner by dedicated leveling up of one stat and then, when getting to a boss, find that you put too many points into something when you should have been getting a bit more of another thing.

I wouldn't worry too much if you had problems with Bell Tower Gargoyles. It sounds like you're new and are getting used to Dark Souls and how it plays. Just continue to level up what you think works. I could tell you what would work for your character and what stats you might want to focus on, but you're more interested in playing the game without guides, it seems.

Continue to level up what you think you'll need. The game is harsh and will teach you what you need at certain times. Don't feel bad about going to a safe place next to a bonfire and grinding out souls against enemies that are easier for you. You'll find a few places in the game are useful for this (Forest after the gate, Anor Londo Silver Knights) to get the souls you need for a few levels in something to even you out. While the game is harsh, it is fair and won't make it impossible for you to continue on. You'll just have to take some time, think things through, train if needed, and breath.

No, it's not possible to really mess up a non-PvP build. Robert Boyd called out this facet of the game design in his analysis of Dark Souls:

3. It's difficult to truly mess up your stat progression

Dark Souls lets the player allocate their stats bonuses from level-ups however they wish. This gives the expert min-maxer a great deal of flexibility to create the ultimate Dark Souls destroying machine.

But what about the less experienced player who doesn't know what they're doing? No problem -- the design has taken that into account as well. There are several effective tools available to the player that have little to no reliance on stats, like elemental weapons, armor (armor increases weight but doesn't have specific stat requirements), and powerful fire magic called pyromancy, that the player can use to dig themselves out of the hole they've created with poor level-up choices.

All level-ups give a slight boost to the player's overall defense, so no matter what you choose, you're always getting slightly more resilient. And it's possible to max out all stats eventually -- so in the end, poor choices can be fixed with grinding.

However, PvP in Dark Souls is level-banded - a level 10 player won't fight a level 50 player, a level 50 player won't fight a level 100 player. If you want to be competitive in PvP at a particular level band, then yes you'll have to make sure the character is built in a particular way by the time you reach that level.

You can mess up your ideal PVP build.
You have to understand that once you reach a certain point (I think it's 50),the bonus you will get for every points added will decrease majorly.

So if you set a lvl cap for you build (pvp build - a common pvp level is 120-130) it is possible and easy to mess up you build.

That beeing said, you should note that it is possible to clear the game without leveling up at all.
Also, the maximum level is somewhere around 711. Note that this varies depending on your class.

I'm not saying that with a regular player you can't do any pvp but in my example i'm thinking Pvp Dedicated Build.

So depending on how you see it, it is possible to mess it up but if you are looking for a casual playthrough you shoud not have to worry.