It's not that low-VOC odorless paint is the only option, but you're right that it's worth looking for if solvent fumes give you headaches. The thing is, "odorless" and "low VOC" don't always go hand in hand - some brands smell less but still have something, and others are genuinely odorless but cost quite a bit more. What matters is that you specifically look for water-based paint with low-VOC certification (less than 50 grams per liter), because those are the ones that actually reduce volatile compounds.
As for reliable brands, it depends a lot on where you live in Spain, but people around me who've painted apartments have used Caparol, Dulux, and Bruguer without major issues. Caparol has a specific line for interiors with very little smell that people tend to recommend on DIY forums. You can also ask at local paint shops - the staff have been watching people paint for years and know what works without leaving your apartment smelling like chemicals for a week. One thing I learned watching colleagues paint is that ventilation during and after is still key, even if you use eco-friendly paint, so keep that in mind.
The best price-to-quality ratio usually comes from mid-range lines of big Spanish brands, not necessarily the most expensive ones. Try comparing at local hardware stores before buying online, because some sellers have promotions depending on quantity and can advise you on how the product actually performs in enclosed apartments like yours.