Traveling on a Schengen Visa between European Countries

I am traveling for work to Brussels, Belgium and have to stay there for about 4 days. I had added 3 more days for sight-seeing to my itinerary, so that I could visit a few other cities around that country. This was a couple months ago when I had applied for a Visa. So I had already booked a to-and-from flight.

However, now I have a friend over in Madrid who has been hospitalized and I thought I could visit them instead of sight-seeing for the 3 days. My friend was pretty helpful when we were together and so I thought it would be nice this time to check on them.

I hadn't planned this before, while applying for the Schengen Visa, and so was wondering if someone here could tell me if taking a to-and-from flight between Brussels and Madrid would be an issue? Would I have to go through immigration again when traveling from Brussels to Madrid and then back again?