Honestly, if his tail appears to be frayed and whitish, it might not hurt to add a bit of salt pre-dissolved in water and (the natural antifungal) Pimafix, if you have any, while you're waiting to find out for sure.
That and trying to determine if the red streaks are an infection that requires emergency aid or just colouration.
Although white edges can be regrowth of damaged finnage, the frayed aspect does give one pause.
And the short-term use of salt and Pimafix, without being as toxic as most anti-fungals, may help to slow or halt the progress of any fungus, should this be the case, and not be harmful, in any event.
Granted, I'm a little paranoid, having a betta suffering from a horrible black fungus, but while one doesn't want to randomly medicate, one doesn't want to leave a potential problem to get worse eiher.
There is an emergency forum for sick fish, and f you could post there and get the advice of someone highly knowledgeable like Wilder, any such issue could likely be identified and dealt with more rapidly.