Will this work to pick up radio?

It'll pull in something, but the soda can isn't doing what you think it's doing. At FM frequencies a reflector needs to be sized to the wavelength, which is around ten feet, so a chunk of soda can taped to wire is basically just decoration. It's not hurting anything, but don't stress about which way it faces. Facing the towers, away from them, it won't make a real difference at that size.

What actually matters is the length and shape of the wire part. FM broadcasts roughly between 88 and 108 megahertz, and a half-wave dipole for the middle of that band works out to about 60 inches of wire total, split into two 30-inch arms. So take your copper wire, cut a 60-inch piece, fold it in half at the middle, and pull the two halves out flat so it looks like a big T with the arms spread wide. Connect the middle point to one antenna terminal and one arm end to the other, or if your receiver has a single 75-ohm screw terminal, hook the center there and let it hang. The little T-shaped wire dipole that came with your receiver is exactly this same idea, just made from flat ribbon instead of copper. Your diamond web shape will still receive, since any chunk of metal picks up signal, but the spread-out T is what the receiver's tuner is designed to work with. That's probably why holding your loop near the terminals seemed to help. It wasn't your imagination, you were just coupling some extra signal in by proximity. At 15 miles from the towers you should get clean reception with a proper dipole, no amp needed. Mount it as high as you can, spread the arms horizontally, and rotate the whole thing so the arms are broadside to the towers. If two stations come from diffrent directions, split the difference and see what sounds best. Solder it up and try it, and if one direction is still noisy, a few degrees of rotation usally fixes it.

The shape you choose isn't the biggest hurdle; making sure you have a solid ground connection is what really makes or breaks it. You can string a wire loop up and if the ground is poor, the receiver is still just going to hear noise. Most folks forget that basic setup. I used to run a full copper stake into the dirt for good coupling, expecially when pulling signals in areas with patchy coverage. Just hang that thing high and hook it right to a real earth connection.

I found that even if your wire shape is perfect, placing it too close to the house or the metal siding can ruin the signal. I always try to get the whole setup mounted outside and away from the main structure becasue nearby metal gets in the way. The biggest trick I learned is keeping the feed point clear of any other wires or pipes. If you're running a long run of copper, make sure it isn't tangled in a basement bundle or anything similar. I’ve had wires that worked great til someone decided to reroute the plumbing nearby.

I totally agree with the point about keeping the whole thing away from metal. Any nearby siding or plumbing is just going to add interference to your signal, which is frustrating. When I set mine up, I made sure the entire wire span was positioned at least five feet away from any structure. Getting the height right is huge, because you are trying to pick up signals coming over a long distance, and keeping those receivers clear of the immediate enviroment helps a ton.