How to troubleshoot HVAC for room that is uncomfortably warm in both hot *and* cold weather?

I have a room in my house that I spend a lot of time in. It is consistently uncomfortably hot in the summertime. A thermometer on my desk will read 80 degrees or more in the summertime. I was told that the HVAC likely isn’t pushing enough air into the room. I was told that I could pay thousands of dollars for a "mini-split" that would push more cold air into the room. As an alternative, I purchased an evap cooler which works well enough, but at the price of frequently refilling it and keeping the door and window open, which compromises my privacy and comfort.

Now that the mercury is dropping, the evap cooler is in the closet, and it is still uncomfortably warm in this room. The other day, I was on the phone and I noticed my forehead was sweating and the reading on the thermometer was 82. This seems to mean that the same HVAC that was pushing "not enough cool air" into this room is now pushing "too much warm air" into this room. I’m paying money for my HVAC and alternating between sweating my brains out and leaving the window hanging open so that I have to listen to every barking dog in the neighborhood.

All adjoining rooms in the house are a comfortable temperature all year round.

I suspect that if I had purchased that "mini-split" to get more cool air in here, I’d still be unhappy that this room is so hot in the winter time.

What kind of problem am I likely having that a room in my house is uncomfortably warm in both hot and cold weather while the adjoining rooms are all comfortable?

Here is some more information requested:

In answer to some questions that have been brought up, the room only has a single south-east facing window. It is an ordinary room surrounded by ordinary drywall, like all the rooms with south-east facing windows that are comfortable all year long. The room is directly above a kitchen that I have never had an HVAC problem with. The ducts run between the two floors, so it is impossible to take a look at it without tearing holes in the ceiling below.

There is a single compressor that cooler the whole house in summer. There is a single furnace that cools the wholse house in winter.

There is a single vent blowing air into the room. We had an HVAC duct cleaning company in the house a while back. The guy who recommended the mini-split said that duct cleaning companies can be good at finding if there may be a break in the system that causes air to escape.

I want to emphasize that I am not an HVAC expert. I am handy enough to tackle something from time to time when I have the time and motivation for it, such as when I replaced the blower motor several years ago to avoid paying an inflated price to have a contractor do it. I don’t know all the lingo, but I will do my best to answer questions to help solve my problem.