Medinilla is an uncommon indoor plant because its requirements are difficult. Primarily it needs lots of high humidity at all times. The pebble tray will help some, but may not be sufficient, depending on how dry the air is where you are. A humidifier may be necessary. Daily misting does little to increases humidity.
Its other primary requirements are warm temps and lots of very bright but mostly indirect sunlight. Imagine a greenhouse environment and try to duplicate that as best you can.
Normally, it would be in a semi-dormant period with a bit drier soil and lower temps at this time of year, but I see yours is now in bloom so it is out of its normal cycle. It may be that the neglect at the nursery actually helped bring about the flowers.
The damaged leaves are no doubt due to cold, the irregular watering, and even some physical mishandling. The leaf spots that you see may be nothing more than the initial symptoms of that particular leaf dying back gradually and you may not be able to prevent that. It is not a disease that can be arrested by cutting out the brown spots. As long as new growth leaves come in and remain healthy, then you are on the right track.
I often preach about not repotting unnecessarily, but this is a plant that especially needs to stay quite potbound if you want it to do well and bloom regularly. There is no reason to repot it now or in the foreseeable future. It does best in a very porous epiphytic or Orchid potting mix. Keep the potting mix well hydrated, especially when the air is dry.
Overall, your plant looks quite healthy given its prior mishandling.
