Actually removing swirl marks and scratches is referred to as "paint correction". It requires training, a medium amount of skill, and access to a full range of different polishing compounds and tools to do it properly. Do it improperly, and you risk doing more damage than you fix. And once done, you need a very careful and disciplined cleaning process or the swirls will come right back.

Your best bet is to use something like Meguiar's G6207 Black Wax Paste. That will (temporarily) fill the swirl marks and give you a nice looking shine. You'll probably need to re-do it each time you wash the bike, but a bike frame is so small that waxing only takes a few extra minutes. It's slightly more work than a spray, but you'll get much better results. A 7oz tube will set you back about $12 and probably last two years or more. Yes, there are much "higher quality" (more expensive) products out there, but using a concourse quality wax on a bike frame is a little silly.