Ventilation fan is probably beginning to look like a pretty good deal. Functional ones are available for under $25. It sounds like the lack of moisture removal is compounded by not using moisture resistant drywall in the renovation.
Recommend you get things dried out and install the ventilation fan. You should scrape off any loose paint and bubbles then when dry, use a semi-gloss bath and kitchen paint rated for moist conditions. For example Moore’s K & B Paint for Kitchens and Baths 322 can be used over clean glossy surfaces and resists the growth of mildew under humid conditions. This would offer protection and prevent molds in the area.