My Betta fish, which is a beautiful Red Double HalfMoon Tail, has started to show a clear tip in his fins. What started out as a few mm has now turn to a cm worth of clear tip. I have read this is fin growth. I'd like to make sure he doesn't have fin rot.
Yup, Silverfang is correct. Clear to whitish for new growth, black and crusty/flaking for rot (some rot can have tufts of white at the tips, but it won't look anything like what you are describing but instead hanging off the tips).