A The recommended dose of Botox to the 11's per the manufacturer, Allergan, is 20 units. It is normal and expected for patients not to see results the following day. Botox results can start to show around day 4, but will not reach full effect until day 14 after injections.
If you have deep, "moderate to severe" 11's and show deep creases while your face is at rest, then you will most likely need combination therapy for the surface on the skin too in order to "get rid of" those lines. You should be able to talk to your provider about options such as: micro-needling, microdermabrasion, chemical peel, derma-planing or possible lasers.
Stay in open communication with your injector so they know how to help you meet your goals.