piano practice - do I need a teacher?

Yes. You do.

Self Teaching

You can't afford a teacher? Well, plan to get one some day or you'll be shorting yourself.

You're already smart and motivated enough? Me too! So I ...
Decided I could. (I've learned 8 computer languages. Easy.)
Bought keyboard, watched videos, read books and websites. Learned tons.
Learned 4 songs over a period of 2 years (not bad).
Played them so many times that my family plotted my death.
Dreaded learning any song longer than 3 pages.
"practiced" a song by playing it through. (Queue laughter from experienced piano players.)
10 years later - hadn't learned much new in the last 7 years.
Decided to try out a piano teacher.

So I Got A Piano Teacher

Found a piano teacher that "clicked" with my personality. I'm weird.
Got forced to do things against my will. Realized later that it was not against my will after all.
Had a new weekly "don't be a slacker" deadline. Every week.
A hell of a lot more fun.

I'd done fine teaching myself, what with not being an expert and all.
But I would have been 7 years further ahead starting out with a teacher.

Your Coach

You need someone that
knows you.
knows what you can do now.
knows what you want to be able to do some day.

and calculates a prioritized list of skills to get you there. Skills that she has already learned and is good at getting across. Each week, you get the next chunk of things in that list.

Piano involves a lot of skills happening at once. And you need a coach to show you where things need work. You may find those things listening to your recordings. But you may not. In fact, your brain will lie to you. Your brain knows how it should sound. And if it doesn't actually sound like that, well, your brain isn't paying attention to how you actually sound. Most beginners think they sound great. UNTIL they play for an audience. Then they know.

What you get

A mentor who can play the piano way better than you.
A regular due date that forces you to practice so you don't look like an idiot at the next lesson.
Someone to teach you fingering, smooth moves, how to make it sing.
An extra pair of ears who watches out for crappily played notes and suggests ways to play them un-crappily.
Somebody to nip bad habits in the bud. Otherwise they're in all your songs.
Somebody to cheer you on. Your family will not.

It's your job to pick good music and get better. But a teacher puts you on the fastest possible path. Time is of the essence playing piano.

The Click

Not all piano teachers are alike. You need to find one that fits you.
So try out at least 3. Pick the best click.