A wire brush is too large for these small spots. You would damage the area around it. You do not have to remove the drain.
First clean the whole area with whatever mild abrasive cleaner you have been using. Scrub carefully with cleaning powder and a soft cloth. Get the abrasive powder out of the rust, then dry with a cloth.
Then put a dab of porcelain paint on it as is. Or try to remove the rust with a very abrasive eraser stick (like we used to use with a typewriter) and then put on the paint. The paint color will not match and will show, but it will look better than the rust and the rust will be stopped for a long time.