The awfulness of this post is pretty remarkable. Sidestepping the wrong "your":
*) This antibiotic isn't for "taking", it's for things that aren't edible like soap and toothpaste
*) Overuse of antibiotics doesn't "raise your resistance to them", at best it increases the bacteria's resistance to them, but in actually it just increases the chance of creating an antibiotic resistance strain. Almost all of the time, however, any resistant bacteria that may develop are killed by other means (like your immune system) and don't live on.
*) One should never save antibiotics, but rather take them when prescribed and as prescribed. While your post could be construed as saying that, the reality is that antibiotics generally require a prescription so it's unlikely anyone will have any to save unless they were sick but are feeling better halfway through the prescription. Saving them at that point is the worst possible thing you can do; not taking a full regimen is what is primarily responsible for resistance.
All that being said, the first point is the most important: this is an external antibiotic. Since it's not applying evolutionary pressure while the bacteria are in your body, there isn't a combined force to make deadly resistant bacteria: ones that survive the antibiotic may not be as effective in the body and thus no one cares. Further, even if that is not the case, the mechanism of action is not the same as other antibiotics so it can still be killed off effectively. For instance, MRSA which is resistant to basically every internal antibiotic can be killed by Triclosan (the chemical in question).
It's very important to understand that not all antibiotics are the same. Something like a blast furnace will kill bacteria and they will never develop a resistance to it, period. However, it will also kill all of humanity so it's not a fantastic treatment for infection. Ditto with chemicals like ethylene oxide or other physical means like gamma rays. Something like bleach is also very effective at killing bacteria, and can even do so on human skin, but obviously doesn't leave the skin doing so well on longer exposure. There are many many things that kill bacteria. The only ones that are really 'special' and need careful use are the ones that can kill bacteria without killing people. Triclosan kind of falls in the middle and while it deserves some consideration, that 'ZOMG RESISTANCE" response isn't really appropriate either.