That wouldn't be a good idea. Both meds are heavy hitters. I would choose one or the other. Honestly, the likelihood that you have a bacterial infection far exceeds parasite, but it's your choice what you want to treat for since it could technically be either.
Cycling a 5 gallon with a heater is a great idea and will help him stay healthier in the long run. For now though, he may have difficulty swimming and I would probably not worry about turning on the filter until he's well. With a 5 gallon uncycled you just need one weekly 100% water change. When you do the wter changes, put your thermometer under the tap and adjust the temp until it is equal to the tank's temp. That way when you fill it up with new water it will be as close to the same temp as possible - you may still have a couple of degrees error but that's okay. Make sure to float him in a cup and acclimate him slowly each time to avoid shock.
Cycling will take 3-8 weeks once you start on it and that's not something you want to do with an already sick fish. He needs clean water right now. Plus the meds may harm your bb growth.