Kristen, welcome to the site and there is a fix for you present situation. Vinyl siding comes in 10' sections and is generally a 2 or 3 board piece. They are secured to the wall with galvanized roofing nails. There is a seam where the pieces interlock and you can buy a zip tool that is made for separating the seams. If you are careful you can separate the seams and use a small nail puller and remove the siding without damaging it. When you remove the pieces around the windows number them on the back side so you know which one goes back and where. Piece of tape works for this.
After you get the siding loose or removed make a picture frame out of 1X4" treated wood and secure it to the outside wall around the window. Now you can either paint your picture frame, which will require maintenance over the years, or you can wrap the frame with "trim coil" painted metal. Then run "J" channel around the frame and reinstall your siding with roofing nails. Do not drive the nails down tight but leave them about 1/8" from the siding to allow for expansion of the vinyl, also place the nail in the center of the slot on the lock strip of the siding. If you see warping of the walls on a sunny day the nails were overdriven. It is not a difficult job but will require a little effort and finesse on your part, working on ladders or "pick boards". It will make a tremendous visual improvement over your current install.
Hope this helps. If you think this is more than you want to tackle, go to a local vinyl siding supply house and ask the people at the counter to refer a installer who would do a repair job as you have described. They will have the tools to fabricate the metal trim, but this is something you can DIY.
