That's so funny because I just had my bathroom remodeled and that is exactly how the shower was working when they were done. Cold was hot, and hot was warm. Fortunately, I could call back the contractor to take care of it and he was able to go in there and do something to fix the problem. I wish I could tell you what he did. What I'm trying to say is that it is not something that involves a huge amount of work. There is a disc behind the knob that allows you to set the maximum level of hot and if that isn't installed correctly, you wind up with this debacle we have both experienced. If you don't want to call a plumber, then try contacting the manufacturer of the faucet and see if you can get some guidance (Ours is Delta). There's also a good chance there's a YouTube video out there although YouTube led me to think the problem was much worse than it was.

You need an adjustment in the valve that takes about 10 minutes. I couldn't begin to describe it, but I did it about 6 months ago.

Take a look at Section 4 "Installation and Adjustment of the Rotational Limit Stop" to see how the adjustment of maximum temperature is done on a Delta faucet. Perhaps you need to find the instructions for your faucet and do something similar.