He is on the chilly side. I would raise it a couple of degrees. This will help with constipation. I would also fast him the next 3 days to a week until he poops a lot and the bloat goes down.
After that he should be fed two small meals a day (one am and one pm) 2-3 pellets at a time, and one fast day a week.
Also I'm sorry but you can't cycle a tank of this size. It's just too small to ever establish, and , and trying to do so just stresses your betta because there is no way for him to get away from the current created from the filter.
I would remove the filter. Your bowl now needs three weekly water changes, of 50% 50% and 100%.
The 50% changes the betta can be kept in the bowl and use a turkey baster to remove half the water and as much of the debris as possible. For the 100% you need to remove him - scoop him out with a plastic solo type cup and set aside while you thoroughly rinse the bowl and gravel to remove the debris. Then he should be acclimated to the new water by floating for an hour while you slowly add a couple tablespoons of new water to the cup every 10 minutes. When you release him, try to let as little of the old cup water back into the tank as possible. All water changes should use same temp water, matched to running tap using the in tank thermometer and the water needs to be premixed with conditioner before adding it to the betta tank. If you don't already have anything, you can use gallon water jugs from the grocery store - rinsed thoroughly in hot water but no chems.
If you want to try cycling a tank I suggest getting at least a 5g, as even double what you have is unlikely to fully establish.