Jana, we are so happy to hear that you're enjoying the game so far! 鉂わ笍
It sounds like you might have hit a bug that I remember Jakob writing a fix for, but maybe that patch wasn't fully released yet. Sorry for your bad luck! Here's what I think is happening: the first time you enter the room with the Rainbow Golem, you can't hurt it yet with just your bow. He's a big rocky monster, so your arrows just bounce off of him. Past him, you get the bombs and then need to go backwards through that same room again, but this time the doors automatically lock behind you in order to force you to fight him this time around, now that you have the bombs. Here's the nasty bug, though: the doors only open back up when you blow up the Rainbow Golem, but if you throw your bombs really fast, you'll blow the Golem up before the doors lock in the first place, and then they lock afterwards, leaving you trapped inside with no other way to get out. It's not your fault, you're just too good of a player, and those bombs are fun to throw! I'll bug Jakob about making sure the fix for this gets released. Until then, the next time you play, try making sure you go all the way into the room first and wait to hear the doors lock before you throw any bombs at the Rainbow Golem, and you should be fine.
You're right that the game doesn't support saving yet, but you don't have to start over entirely. The next time you launch the game, you can pause it right away by pressing the p key, and while you're in the pause menu, press the down arrow until you hear "Debug," then press the spacebar, and then press down until you hear "Teleport to dungeon." If you press spacebar again, you'll start the game right in front of the entrance to The Mines, with your bow. You won't have the bombs yet, so you'll need to repeat a little bit of the area, but it will save you from having to chase down chickens in the Village all over again 馃槉.
You were already pretty close to the end of The Mines, there were only a few puzzles left, so you can also jump directly to the end boss if you'd like. Instead of selecting "Teleport to dungeon" in the pause menu, you can select "Teleport to boss," and you'll jump to the end of The Mines right before the final boss fight. Best of luck, we really hope you're able to beat the game, and please let us know if you need any more help!