As von behr has said, trout can be picky. However, IMO moving water can be more of an issue than the fish if you're not used to fishing it. Not all trout are picky. There can be advantages to fishing in current, but unless you're casting technique is solid, you'll likely do better on stillwater until you become proficient at casting. Take away as many variables as possible & learn one step at a time. I can certainly agree about fishing for Bluegills. I spent many hours catching them as a kid, still enjoy catching them & they helped teach me as I progressed.
I'm self taught too, and have had some additional instruction that aided in correcting bad habits I had as a result of being self taught. Watching the back cast can be a good way to get a good forward cast if you're having issues. Another problem that beginners may have is attempting too much distance. First, it's often not needed to catch fish, and second, until you've mastered the basics of casting, the longer distance you attempt, the less line control you'll have, both during the cast & on the water. Add the problems associated with moving water, and it's likely you have almost no control of your line or fly at all. Without control, even if the fish are taking the fly, it would be difficult to set the hook & catch many.
Casting instruction will no doubt help. But, not everyone can afford the cost. (Some shops will give free instruction, take advantage if you can!) So, take it slow & work on your casting frequently. The video's should help & each time out, think about the problems & go back & review the video's with the thought of why you're having a particular problem. Don't get too concerned over catching right now, and concentrate on your casting, and how it relates to the fishing of the fly.
Just some examples, if your line is not landing in a straight line, or may be landing in a clump. Perhaps you're back cast is hitting the ground (or water) behind you. Or the leader & fly are not landing straightened out from the line, or perhaps the fly is slapping the water when it lands. These are all common problems that beginners may encounter.
Learn from your mistakes! IMO, we often learn much more from mistakes & bad days fishing than we do from the good times. In the end, it will make you both a better caster & a better fly angler!
BTW, there is a member, "Silver Creek" who has always posted excellent information. Some may be very technical but a lot of his posts can be very helpful to a beginner. Search through the site & find his posts & pay attention to what he says about both casting & fishing. Coupled with various videos, you may find that his explanations will aid in figuring out on your own some the ways to correct problems you may have.
I'm sure he'll chime in too & add some additional advise!