One of the most prevalent fallacies in human development is the idea that if you respond attentively to your young children, it will form them into weak self-centered dependent adults.
The research indicates the exact opposite. When children experience emotional attunement and responsiveness from their caregivers it helps them feel safe, which in turn helps their brain develop more awareness and complex focus in relationships. When children's emotional needs are ignored, they develop heightened fear states that make it hard for them to learn the nuances of relationships. (check out the strange situation studies, and Es Tronick's Still Face Experiment, and the Adult Attachment Interview, and all the longitudinal studies done with all three tools).
You aren't spoiling your child when you comfort them, hold them, respond to them, and treat them with the same respect you would want in a difficult or need based moment.
Ignore the judgment and follow your instincts for care. I promise you won't regret it.