Your biceps work hard, but so do your upper back and rear shoulder muscles. The key is to learn how to do this coordinated arm-back muscle pulling work. There are many kinds of rowing machines. You can also ask a trainer how to row with free weights. These exercises put the biggest emphasis on the sides of the upper back.
Static contraction exercises.
This is an alternative to the standard sets and reps. Using weights or immovable objects like walls and doorknobs, you can hold contractions for extended periods. 34 pounds at 20 months can be a constant challenge. The thing is you're probably holding him with one arm, and wrestling with a bag full of toys in the other. The untrained bicep and forearm will feel the strain in no time.