i'm a single parent, with two fish tanks and two chinchillas. all my pets get individual attention every night, and my tanks receive water changes on a daily basis if and when necessary. every weekend i schedule in at least 2 hours to ensure both my tanks get a good water change and necessary gravel vacuuming/filter cleaning. my kiddo goes off to play with toys, or watches tv, or plays on the computer. or i do water changes after she's in bed. doing a large water change on a 5ish gallon tank is nothing! should take you 20 minutes at most.
there are other parameters that you are not able to test for with your kit that could affect your betta's health. TDS (total dissolved solids) and DOC (dissolved organic compounds) build up in the water between water changes, causing water quality to go down. with the recent medications in your tank, your beneficial bacteria could be not at sufficient numbers any more to handle the wastes of your betta (remember how i said some meds will kill that good bacteria?). daily water changes are the best thing right now, to keep the ammonia down and keep the tank clean for your recovering fish.
the most important reason for you to do daily water changes right now is because your betta needs the cleanest environment possible to recover from what is/was ailing him. many times clean water is a great cure, and all that is needed. i've seen a large shark here on the forum with huge wounds be healed just by daily water changes.
plop your kiddo in front of the tv for a half hour show once every day, and get those water changes done
edited to add - your test results you posted previously say ammonia is zero, nitrite is zero, and nitrate is 10. now you are saying all three parameters are zero? if they are all at zero now, then your tank is not cycled and daily water changes are a must to keep the ammonia from reaching toxic levels for your betta. zero for all three tests tells me the meds did knock out all your beneficial bacteria. your tank willl need to re-cycle, and daily water changes and daily testing will keep your betta healthy.
also to add - constipation in bettas can be helped by feeding them a small bit or two of the inside of a pea. pop the pea in the microwave for a few seconds to soften it up, then split the pea in half and take out the inside part and make it small enough pieces for your betta to eat. this should help the constipation. the white dot could be some muscle that has been pushed out of place due to constipation.