Should I be worried about spoiling my baby?

No. New babies just want a few basic things: food, protection/love, and to be clean. They need us at this age, and want us to be there for them. So, by holding them when they cry, or feeding them every time they are hungry, or changing their diapers when they only have a little pee stain will not spoil them. We all need more love anyway.
No. I prefer to use the term with fruit not picked up on time. Why it applies to coddling babies i don't understand. We teach babies they are worthy of love and attention by providing unlimited amounts. That term is often used by minor players in babies life who are offended when baby doesn't relish time with them as much as their parents. Shame on them for their shallow comments.