In USA and some other countries, eye doctors are required by "Eyeglass Rule" to release a copy of your prescription after each eye exam at no extra cost. In 1978, the Federal Trade Commission passed a regulation rule known as Ophthalmic Practice Rule, or Eyeglass Rule. The rule requires eye doctors (optometrists or ophthalmologists) to give patients their eyeglass prescriptions at no extra cost. Based on the rule, you can ask for a copy of your prescription from your eye doctor after an eye exam. You can ask them for prescription and then place your order online.
If you have paid for the complete exam, the doctor have no right to refuse to give you the prescription. You should go back to your doctor and ask for your prescription. If he refuses, just tell him that you know the law. Then he will give the prescription to you.