BA comes into T4S, most IB comes into T4. Air Nostrum departs from the high K gates in T4.

It is doable if on time or up to 15 minutes late, I'd say. You'll need to walk up a series of ramps to get to the arrivals level of T4S, walk along to immigration, down a few levels to the transit, up a few more levels, exit the lift in baggage claim, right and right again to security, up a level to departures and a left turn to the high K (blue) gates.

Try pricing up in Google Flights to see if you can get the IB codeshare and the earlier flight to ALC.