Is it true that I could spoil my baby by picking him up every time he cries? It just gets frustrating when he keeps crying.

No dear, you are not spoiling him infact this kind of attachment parenting is necessary for of the baby . Babies always cry when something is wrong, they are not able to self regulate their emotions like adults. Outside world is really confusing for them and they need the smell, touch of their caregivers to calm them down. So please take full care of your baby because he needs you the most right now.