Regarding your boyfriend's comment that the heat the turtle is getting "is not like regular heat and you can't feel it,"... heat is heat.

You can check the basking area temp with a regular thermometer. Just put it on the basking area under the light where your turtle would be basking (or put a rock the size of your turtle there and put the thermometer on that) and leave it there for about 15 minutes or so. Then take a look at what the temp is.
I looked at your link, and I'm assuming you have the Reptisun 5.0 tube (doesn't say it's tropical, though) and that's OK for a UVB light. I don't think it gives off enough heat, though (as checking the temp with a thermometer will tell you), so to increase the temp., you could just clamp a regular lightbulb over the basking area (get a clamp lamp with a dome). Don't just go by wattage, use whatever will keep the basking area about 88-90F (water temp should be about 76-78F, and you can get an aquarium theromoeter to check the temp); you can adjust the basking area temp by either using a different wattage bulb or moving the bulb closer or further away from the basking area depending on if it's too warm or not warm enough. Ideally, you want to have the UVB light as close to the basking area as possible (or part of it over it). Barriers like glass, plexiglass, screens, even water to some extent will filter out UVB rays and your turtle won't benefit. Try to have the UVB light no more than 12 inches from your turtle.
If you upgrade, try to go bigger than 55 gallons--Louis is 5.5 inches now, but when he grows, that 55 gallons will need to be upgraded as well. And if you go bigger now, you won't have to do it so soon.
I've never used a Cascade filter, but it doesn't sound like it's even big enough for the 20 gallon tank you have now (and if its internal, it's wasting space in the tank). A filter rated for a 60 gallon tank (or at the very least a 40 gallon tank) would keep the water much cleaner. But if you go for a 55+ gallon tank, get a canister filter like the Filstar XP3, Fluval 404, etc. (There are posts on these filters and others if you look.)
G.P.H. means gallons per hour, so if yours says 110, it pumps 110 gallons per hours. (Just to contrast, the XP3 pumps something like 375 gallons per hour.)
You can buy a Python at petstores, but more cheaply at Walmart (the 25 ft. long one, anyway). They're easy to use, and you don't have to lift the tank. Hope this has helped as well..

"You become responsible, forever, for what you have tamed." -Antoine de Saint Exupery-