Well, first of all not to worry that you fell off. everybody falls off, sometime.
Perhaps you should stick with the rising trot for a bit. Or, do a few strides sitting, then go rising (posting), then sitting, then rising.
Remember if the horse starts to go too fast for you, you can always circle him to slow him down.
If you can ask your instructor for some lunge line lessons. This is the old fashioned and most excellent way to work on your seat. Riding the sitting trot without stirrups and with your hands free to hold onto the saddle (while horse guided on the lugne by your instructor) is an excellent way to build skill and conifidence. Every 4th lesson should be a lunge lesson, in my opinion.
Ask about it. but be sure to use a quiet , reliable horse for the lunge.