Cradle cap. Baby’s head is red

My 3 month baby has had cradle cap since 3weeks of being born and I have always put oil on his head a combed out the flakes. Today I decided to do that today because I have not done it in a while and today when I combed it his hair came out as well , Now he has bald spots and his head is red. What can I do to soothe the redness or should I take him to his doctor? I feel horrible I fell like I ruined his hair and put him in pain

His hair now ^

His hair before ^