Hello. Whether you need backup birth control after missing a birth control pill depends on where you were in your pack when you missed the pill. For combination BCPs like Tri-
Sprintec, if you miss one of the first two pills in the pack, you should take the forgotten pill as soon as you remember and the next at its usual time (just like you did). You should then use a backup method of birth control (e.g., condoms) for one week.
If you missed a pill from day 3 through 21 of your pack, you should take the forgotten pill as soon as you remember it and the next at its usual time (as above). Backup birth control is not required in this case.
If you missed one of the inactive pills (the white ones), you don't need to take the forgotten pill, and no backup birth control is needed.
Given those scenarios, you can decide whether you need emergency
contraception. Specifically, if you missed one of the first two pills of your pack and had unprotected sex within a week, you should take emergency contraception. Otherwise, emergency contraception isn't indicated.
I hope that answers your question!