Is it acceptable for a 19 year old girl who is 5' 1 1/2" to weigh 102-104 pounds?

Yes it's acceptable but you're pushing toward the point of being underweight, which is unhealthy for your body. If you were to go under 100, according to the BMI chart, you would be underweight. So 95 really isn't good for you. I suggest you don't go lower than 100. You should already look way past beautiful anyways. Maybe go get some counseling for this? You may become anorexic if you don't, if you aren't already anorexic anyways. I hope you will feel comfortable in your body. Good luck to you.