If you could please post a couple of close-up pics of the tail itself and the end of the tail so we can see the issue clearly it would be very helpful.
Obviously she is shedding her entire tail right now, hence the white tail, but the end portion with the two links isn't normal, you're correct, but it's also not quite an emergency...Yet. It is most likely retained shed in the two spots where the kinks are. Think of retained shed on the end of their tails like rubber bands, as this is the best analogy I can think of. The retained shed eventually cuts off the circulation to the portion of their tails below the retained shed, and if not removed then that portion of the tail will become necrotic and typically dry up and fall off. I'm sure you know that Beardies do not regenerate their tails or limbs, so that part of the tail will be gone forever, but not a huge deal.
Where this can become a huge deal is if a bacterial or fungal infection sets in to the area around the retained shed. This happens because there is little to no circulation of blood to a portion of the tail, so it becomes perfect for bacteria to invade because their immune system can't fight off the Infection in the area with no blood flow. This is when tail rot happens. Tail rot is basically a vicious cycle, infection sets in, kills tissue, the dead tissue falls off but the Infection moves right up the tail, killing the tail all along its way, until the Infection hits the body, the Infection then becomes systemic (Sepsis) which is typically fatal if it reaches that point.
Your beardie's tail certainly does not have tail rot at this point, but it's very important that if it is retained shed (I'm pretty sure but need the close-up pics) you get it off of his tail and get some topical antibiotics or raw, unpasteurized honey on the area ASAP, as to prevent tail rot from starting.
I'd be doing warm soaks daily and using a very soft-bristled toothbrush (baby toothbrush works well) gently try to get the retained shed off of what looks to be two different locations. The warm water soaks and the brushing should get it off, though it can be difficult so keep at it, maybe soaks twice a day. Then dry her completely and apply either a triple antibiotic ointment like Neosporin or raw, unpasteurized honey (not regular honey, only raw, unpasteurized, unfiltered honey) all around her tail, from the very end of her tail all the way up to a bit above the effected area into the good tissue, just to make sure you cover the entire area. Hopefully this treatment will not only get the retained shed off but will also prevent any infection from setting in, or treat any Infection that has already set in. She may lose that entire part of her tail, as it may very well turn black, dry up, and fall off, but as long as you keep applying the raw honey or the triple antibiotic ointment throughout the entire process daily it should keep it from spreading upward.
Again, we need close-up pics because we cannot really tell if it's 100% retained shed from the photos you posted.