All you had is an algae bloom from the water that's normal. We call it new tank syndrome. Vinegar not necessary to clean at this point. It's good when you have mineral deposits with age to get rid of. Correct way would of been to have tank setup a month before you got the turtle so water could cycle. In a pinch turtles are hardy and breath like us so it would not hurt it to go right in. A tank not cycled will kill any fish !!! That bottle of bacteria they gave you is ok but it only helps to cycle a tank not over night. Cycling takes minimum of four weeks to do it correct or longer depends on size and setup.
Find another LPS... a better one that really knows something !
Also did you use any water conditioner to remove the chlorine in the water? Do you have any carbon in filter to remove the chloramine ? If not you can burn the turtles eyes ! I'm going to give you a link on this site its under urgent care BUT copy/paste questions and answer in some details. Example : have UVB just don't say yes. give type size / % /wattage please.
This is NOT urgent but the questions will help me help you !
viewtopic.php?t=2142Turtles are great but it sound like you have a lot of homework to do. Read the informational stickies on this forum will help , they are at each topic.