It depends on the layout of the house, and the direction of the wind. If the fumy room has windows, it would be best to open those, and position a fan in the open doorway blowing in to the fumy room to act as a kind of exhaust fan…unless the wind comes in from the fumy room direction, in which case the fan would be useless in that position.
In the long run, it is a bad idea to keep the fumy room closed up because the fumes will not be able to escape quickly – they will just slowly leak out under the door or through cracks in the building envelope. Ideally, you’d be able to open the whole place up, and let cross ventilation remove the fumes relatively quickly.
Another thing you could do is open all the windows in the fumy room (assuming it has them), close the door, and stuff a rag at the base of the door to block the empty space. This would allow you to ventilate the room while minimizing leakage back to your bed. You’d be surprised how much air can pass through the door undercut.
An air purifier is not worth the extra money for a one time event like this.
Idk what kind of paint enamel is. Water based paint has less fumes than oil based paint. When you buy paint next time, check the VOC content. The lowest VOC content will smell the least. If I ever have my own place, I’d like to try this Milk Paint.