I’m failing as a mother

My son is 2. He’s the pickiest eater ever. He drank a bottle of milk until he turned 2. Not too long ago. His pediatrician said it was fine to stop at 2. My son was miserable and we had some good nights. He needed it plus his binky to fall asleep. We stopped his bottle but he still wanted warm milk . His doctor said warm milk in a sippy cup was okay and use his binky until he’s sleeping then take it out. It’s fine that way I take it until when he’s sleeping but I feel like I’m failing since I can’t get him off the binky completely. He uses it for 10 mins to fall asleep at night than I take it out. The doctor said as long as the warm milk isn’t in a bottle it’s fine.I

Is this accurate? Please someone give me advice all my family does is judge me and tell me I’m not doing a good job .