At least, as a first step, share your piece in a writing group, receive critical feedback and edit and polish the hell out of it. Definitely do that before ever considering submitting for publication, and if you don't attend a regular Writing Group in your area (or start one), then have your Ideal Reader critique it, as wife Tabitha and friends do for Stephen King.
To find opportunities to submit to, I use these, both free by email subscription:
The first and hardest to use, but most fruitful, is CRWROPPS, which stands for Creative Writers Opportunities List. It's a daily Listserv. That's its' glory and downfall: they're so many opps, you'll receive a dozen daily. But it's worth going thru them, deleting the non-applicables, and red star or note the most promising ones. Heck, you may even find a teaching job! Then go back and select the one(s) that absolutely fit you, and Submit! (And don't spend more than $15 per entry unless you're wealthy. See my earlier Post on what to look for and what to avoid.)
Sign up by joining YAHOO! Groups at https://groups.yahoo.com/neo/groups/crwropps-b/info
The other excellent method is signing up for almost daily updates from Funds for Writers Blog and website by C. Hope Clark. Here's the info they put out about it: