The ideal solution for you would be a permanently installed mini split air conditioning unit.
Those allow using AC with all windows and doors closed, so they are generally very energy efficient because they remove heat from indoor air and blow that away in the outdoor unit. So the indoor air (which may be cooler than outdoor air) won't be blowed outdoors, to be replaced by a similar amount of much hotter outdoor air. Usually they are quiet as well because most of the noise is in the outdoor unit, and many have quite efficient inverter-driven operation allowing true variable performance as opposed to constantly cycling the unit on/off.
About the only problem is that if you live in a rental apartment, installation could be bit tricky. Maybe if you tell your landlord that you will pay for the unit, and it will be a gift to the landlord once you move away, you could get a permission to install.
Another solution, much worse, would be a portable split AC unit. They have a ~10 kg outdoor unit and flexible refrigerant lines between the indoor unit and outdoor unit. You can use such a portable split AC unit only if you have a balcony or live on the first floor and have a door outside.
A third solution even worse than the second would be a two-duct non-split portable AC unit. They take outdoor air, heat it, blow it away using the second duct, and the heat from the indoor air is carried away there. Because they blow in and out the same amount of air, the outdoor air which is usually hotter than indoor air isn't going to be sucked into your room. A problem in these is that the noise is in the indoor unit so it's very noisy.
The absolute worst solution would be a single-duct non-split portable AC unit. The problem with these is that they have only a single duct where they blow heated indoor air out, so a similar amount of outdoor air is going to be sucked into your apartment. My experience is that once outdoor temperature reaches much over 10 degrees Celsius above indoor temperature, these single-duct portable units lose a lot of their effectiveness. A problem in these is that the noise is in the indoor unit so it's very noisy.
In any case, a modern freezer/refrigerator isn't going to create more than 200 watts of waste heat. Even a basic air conditioning unit is going to remove 2000 watts of waste heat. So a real air conditioner is going to not only fix your refrigerator/freezer heat problem, but also remove a lot of heat from other sources such as your computers, your lights, yourself, and just heat conducted from the hot outdoor environment through your walls.