You can force feed your frog--you can also amputate your leg because of a simple cut.
It's more about what you should do. Force-feeding is EXTREMELY stressful to frogs. Andy mentioned it's that way for all herps, which I disagree with in some instances (well, disagree with the degree of when to do it), but for all frogs it's definitely a bad thing and should only be done when something is nearly at the brink of death, which may or may not have been your case here.
I've saved one froglet and a few anoles by force-feeding, but also have lost a froglet and some anoles from the same thing. All were on the brink of death and probably weren't meant to survive, anyway. If you take in the situation, it's very easy to understand how this is stressful for the animal--it being stressful to the animal was always in my face when I tried this.
Frog vitamins are to be dusted on crickets or other food items, not to be directly fed to the animal. Some kinds of vitamin-foods suitable to some reptiles are something the animal comes and eats on it's own, who better than it to judge when it's in need?
When you force-feed an animal you run the risk of stressing an already stressed animal to death. You run the risk of damaging or crushing it, or, in some herps, causing it to lose it's tail or an appendage. You run the very high risk of choking the animal. It really is to be avoided, except when necessary. Even then, it's a risky thing in most cases, especially with small animals. Books show you how to do it sometimes, but that's meant for when an animal really, really won't eat and is dying. It's meant for when a vet has already seen the animal or it won't make it long enough to see a vet without eating.
There are better ways to provide nutrition for a non-eating frog. Soaking it in Pedialyte works, and I've had good luck applying something like Jumpstart to froglets topically when they wouldn't eat. Regardless, your frog seems to be doing better so take this as a future precaution. What's done is done and everyone made it out alive... that's what matters right now.
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Got hips like Cinderella / Must be having a good shame / Talking sweet about nothing / Cookie I think you're Tame 