Come on now, I don't care how inexperienced you are, adding charges to your bill that weren't discussed with your customer is a sure way to get a reputation as either somebody that doesn't know what they are doing or somebody that tries to nickle and dime the customer after they get the job. Either one is not what you want to be known for. Do the job for what you agreed on, that is the right thing to do and the best path to follow.
In the future, start writing up contracts for jobs, and use change orders for extra work. Keep everything in writing because there will come a day when you and your customer are going to be at odds due to poor memories.