Is it possible I'll need to go back for another Botox touchup if the first doesn't work? Is this common for first timers?

It is common for one to need a touch up following Botox, even if its not your first time. Your doc will eventually develop what the right amount is for you. You really cannot evaluate the need for additional injections until you've waited the full 2 weeks. If you are given more before that time, you may regret it if both "touch-up" injections suddenly kick in.

I always recommend waiting 14 days for the full affect to take place before injecting any additional Botox. Your injector will hopefully get to know how your facial muscles react to the injection sites and amounts over time and will be able to get a reproducible pattern set for you.