I really want to record the game but it doesn't seem to catch the actual game in fullscreen, I'm using obs and bandicam.
The game works great and it's just like I remembered it. But since there aren't any in game settings I don't know if there is a solution to this problem.

If you want to record the game in fullscreen - if there is a "graphic mode setup" in start menu for the game, run it and change mode to opengl. If not, then you can try to edit dosbox.conf. Open it in notepad, find the line with output and change it to OpenGL.

Those aren't DOSBox games.