Most things have a vegan equivalent, but some have one that's very expensive or harder to find, and a few have no equivalent at all, such as the medicine above. Just try and do the best you can.
Toothpaste there is a good chance you can get vegan especially if you live in a big city or a developed country.
Sometimes it comes down to whether you are willing to make the effort.I mean,you can make your own toothpaste if you really want.
But personally I think reducing your direct animal suffering and death contribution by 99% is more important than trying to get to 100%. Work your way through stages:
Stage 1: Just by not eating,meat fish and eggs you might have cut your impact 90%-95%.
Stage 2: Cut out dairy and address clothes and toiletries and perhaps you are at say 97%.
Stage 3: If you cut out other things like non-vegan bread, non-vegan pizza bases, some sweets (gelatin) some cakes and chocolate to get to 98%.
Stage 4: If you want, start reading and understanding ingredients on everything and maybe get to 99%. At this point it starts to get more difficult since you have to know whether if a product says benzofolic acid extract whether that is of animal origin or not.. It becomes ultimately a question of where to draw the line between ethics and how much time and effort you want to spend on it.
Another way of looking at it is that if you obsess about getting to 99.9% or 100% you may take your eye off other issues....like relationship with family and friends, environmental concerns, and other things. Don't focus too much on only one issue.
If you can get through stage 1 above and maybe 2 most vegans would be happy. However, note that at this point you should probably call yourself vegetarian or mostly vegan or plant-based lifestyle or something.
Vegan actually means that you are at stage 3 at least and probably 4, so if you are not it may be safer not to call yourself a vegan as some vegans will not agree with that.
Another way to look at is to relax a bit more when you are out of the home. It's easier to address the things I mentioned in stage 3 and 4 when you are at home, and perhaps just try to getto stage 2 in restaurants in foreign countries, for example.
I had to buy a toothpaste in South Korea. The packet wasn't even in English and no-one in the shop spoke English, so who knows if it was vegan. So, I just bought it. Of course, you can also avoid these situations - if you want to - by being more careful in packing, preparation, calling the restaurant in advance, speaking to the host in advance etc.