A literal reading of Genesis 3:16 certainly seems to imply that pain (even pain associated with childbirth) pre-existed sin. However, having tagged "contradiction," it seems you have a problem with pain being described as good. So let's explore that.
Pain doesn't FEEL good; so how can it BE good?
Stepping beyond the shallow machismo behind pithy one-liners like pain is weakness leaving the body or what doesn't kill you makes you stronger, pain certainly performs all sorts of insanely necessary functions. I'll limit myself here to only two general points.
First, growth is painful. I don't just mean growing pains (although that, too). Putting in the hard work to sculpt a beefcake like the Arnold of the 70s is painful, but can you imagine Terminator played by someone who was small? Gross. More seriously, other kinds of growth involve pain. The growth of a loving relationship necessitates the pain associated with conflict and stress. Otherwise, love remains easy and shallow. This kind of pain results in maturation. One commonly-cited example of life without growing pain is the Biosphere 2. In normal conditions, trees are subject to wind that creates stress wood and encourages greater root growth. Without the stress of growing with exposure to wind, the trees in the Biosphere never became strong enough to support their eventual weight. So as they grew in height and weight, they just toppled over. Of course, you can apply this to all kinds of situations.
Second, pain warns you of danger. Pain tells us to pull away our hand when exposed to scalding water or a hot frying pain. Pain helps to create lasting memories that remind us to avoid silly things like petting porcupines, kicking tree roots barefoot, and jumping into shallow ponds. Pain discourages injurious activities. When you live far away from medical treatment (or in a time long before medical treatment was even a thing), simple injuries may result in permanent disability or death. Without the benefit of antibiotics or sterilization, even a shallow cut or abrasion can prove life-threatening under the wrong circumstances due to the risk of infection.
In summation, I think it is simply basic to say that pain is a good thing. Therefore, even if Genesis 3:16 implies the existence of pain prior to sin, this does not contradict God declaring the goodness of God's creation.