Trying to get a novel or short story published is a waiting game. Patience is rewarded. Impulsiveness is not. And the waiting game doesn't end, even after people in the field start showing an interest.
Let me give you an idea:
I started writing with the intention to publish in college. But really, ignoring semantics, I started writing with the intention to publish in high school. But really I started in grade school, when I set out to write the longest story in my third grade class -- an epic eight-part adventure with swords and monsters that was a thinly veiled attempt to novelize Zelda II for the NES. I never finished it, but the idea and the inspiration were there!
Whichever starting point you pick, I've been "writing with the intention to publish" for anywhere from 10-25 years. Granted I went multiple years where I didn't write a thing and lost all sense of my writing voice, but that's still a long time, and it seems like more and more people look at writing as a means to have one's genius discovered rather than a craft to practice and polish.
As a teacher, I tell my students to practice things like math facts, orchestra instruments, and their writing, reading, and proofreading skills. Almost everyone agrees an instrument takes time, but aspiring writers often falsely believe that writing is born solely in the minds of prodigies.
Okay, maybe I'm overgeneralizing.
What I really wanted to get at is that every step you take in the process of becoming a published writer requires waiting. When you finish a story, you have to wait several weeks (at a minimum) so you can read it with fresh eyes. Once it's polished, you have to submit it to an agent (novel) or editor (short story) and wait for a response. Then you have to spend years collecting form rejection letters and waiting for your first personalized rejection (these can be brutal, but put on your rhino skin and take their advice -- they read a lot more than you do) that actually gives you some ideas on how to not suck. Then, you finally get someone who thinks your writing might be worth putting out there. But you're still not done.
Then your work gets shared with others, and someone else finds something wrong with it (they're right).
Then you find a group of people who like it, but they still think it can be improved (they're right, too).
Then you wait for a confirmation that says yes, your work will be published.
Then you wait for the day, far in the future, when your work is finally published.
So yeah, writing means waiting. A lot of it. If you're getting anxious because you're collecting rejection letters, you're already a part of a pretty cool club. There's a lot of frustration and self doubt involved, but if you can stand the heat you'll eventually become part of an even better club of people who worked, improved, and set their ego aside and risked judgment of their most vulnerable side.
Even now I'm waiting. Not on nabbing an agent (DONE!) or on finding people who believe in my work (also done, and isn't this what we all really want, more than money or fame?). I'm now waiting on a submission list of editors my excellent agent put together. Waiting for them to get back to us with what I hope is an offer is the scariest part yet. It's entirely possible that still, after all this work, every editor will say no, and I'll be back to square one. That's a lot more waiting.
The only thing you can't wait for is time to write.