It sounds as if you have seven nights in Spain. That will give you only six reasonably-non-jetlagged days. Your first day may be pretty unproductive, and if you head all the way to southern Spain, you'll be dealing with airports again later in the trip, turning another day into, at best, a half-day. To attempt three major destinations in about 5-1/2 days is over-ambitious.
Barcelona has a lot of sights, many of which require online purchase of tickets in advance to avoid long ticket lines, which makes it a difficult destination for blitz trips. How efficient a sightseer can you be when you have to guess, before you've even set foot in the city, how much of a gap to leave between your entry times? That can lead to bits and pieces of scattered dead time. To me, four nights is the minimum needed in Barcelona, and there's enough to see in the city to justify a much longer visit. And there are good side trips available to places like Girona and Figueres.
I agree that even choosing one additional destination is pushing it when you are flying in and out of Barcelona. Zaragoza (1.5 to 2 hours away) would be my top recommendation for a second overnight stop. Other fairly quick train destinations are Madrid (2.5 to 3.5 hours) and Valencia (3 to 4 hours). Zaragoza and especially Madrid are likely to be quite a bit chillier than Barcelona and Valencia in February.
Spain's best weather in February is in the south, so if you're willing to spend the time on two extra flights and settle for a once-over-lightly visit to two world-class cities, I'd head to Seville. Although Malaga is a nice city and worth a visit on a longer trip, its sights are nowhere near as distinctive as Seville's.
Granada is an option if you prefer a city where you can focus most of your limited time on one fabulous sight, but Granada is at altitude and almost certainly won't be as warm as Seville. Be sure you can get tickets for the Alhambra before committing to that city. It does sell out, sometimes quite far in advance. This is the official ticket website: https://tickets.alhambra-patronato.es/en/. Note the "Low Temperature Recommendations" on the page I've linked to. The "Alhambra General" ticket is the basic, most-popular ticket. The "Gardens, Generalife and Alcazaba" ticket isn't recommended because it doesn't include the Nasrid Palaces, the most fabulous part of the complex.
