You are a buyer's agent, and a buyer directs you to keep looking for properties after making an offer.
1. It's up to you whether you want to continue looking for properties as it really doesn't matter.
2. Your contract states you will not continue looking for property after the buyer's offer is accepted.
3. There is no problem with looking for another property as the buyer can get out of the present contract using the inspection clause.
4. Your contract states you will not continue looking for property when the buyer makes an offer.