Generally speaking, missing or doubling up on a single dose of an oral contraceptive pills is not a huge problem. Many doctors
believe that it is better to "double up" one day than to miss a dose. The effects of doubling up on a dose are usually pretty minor, although you may have some mild nausea, breast tenderness, or similar symptoms. If you did double up, then you would probably be advised by your doctor to just continue taking the pill pack, one pill per day, as before. The only major side effect that I might anticipate is that this could potentially make your period at the end of the pack a bit different (heavier, longer) than it usually is.
Talking to your doctor in the morning, as you are planning to do, is a good idea. They will be able to provide additional advice and also will be able to help you if you experience any side effects or have any menstrual irregularity at the end of your period.
On the whole, though, I think you deserve congratulations for being so attentive to this issue, and for getting right on it! I think your plan is likely just fine, although do check in with the doctor who knows you best.