Hi Jennifer, and welcome to the forum. We are thrilled you chose us as your first forum!
I think I can probably speak for every vegan when I say that we have all made a mistake at least once. When I was new to vegetarianism/veganism I made quite a few in the first months. I say the same to everyone when this happens, and when they come to the forum feeling guilt and shame - don't make yourself feel like the sky has fallen. It was a mistake, and honest mistakes happen; just embrace it as part of your learning curve. Forgive yourself.
So I commend you for wanting to avoid this but I also want you to be prepared: it will happen, someday and somehow. You might be at a restaurant, they take your order wrong and it takes you a few mouthfuls to realise... it could be anything. Maybe you're tired and in a rush at the supermarket and you don't look twice at a new product. Who knows.
But now that we've got the slightly unpleasant (but truthful) reality to one side, there are so many areas of our lives we can veganise that we possibly don't consider in the beginning. For instance there's
transportation (that's a big one!) though not everyone has the practical means to veganise their getting from A to B and we don't expect everyone to buy electric cars overnight. There's our home utility bills (can you switch from gas to electricity etc. how green is your package?) but, again, not every can switch this as easily as they can their diet (and not everyone has control over what services they use!). There's what we feed our pets (if we have pets, or foster animals, or co-habiting animals - whatever you want to call them) since these days there are healthy vegan alternatives (if that's what you want to do; there are other threads here on the forum about the ethics of enforcing other diets on animals). There's your bedding and upholstery (feathers? leather?). It all depends on how far you want to take it. Only this week another thread was calling leather-bound books into question so
it really depends. Adhesives are often not vegan, as well as some paints and colourings. You can even get certified-vegan condoms now. Yep, many condoms are not vegan (pretty gross, if you ask me).
The crux of the matter is that you're committed to doing as little harm as you can, and in that the vegan community will support you as you go forward.