The first thing to consider is that one month is far to early to say that a result is “botched”.     At one month the injury to the area from the injection has not completely settled.  If the area is soft and compressible, it is very likely this will go away.  Another possibility is that you may be prone to swelling in your lower eyelids from things like allergies and if that is that case, the Bellafill injection made that worse it may take a couple of more months, but swelling from that problem will settle as well.
If what you can feel is firm, then this may of concern, but this should settle as the 5 year studies with Bellafill showed that firm lumps almost always settle in time.  Please remember that a half syringe of Bellafill is only 0.4 cc or between 8 and 10 drops so the amount you had injected is very small and by itself should not make too much difference.  If it looked good right after that is almost always how a Bellafill injection will end up looking like at 3 to 6 months.
At a month, my first recommendation would be to be patient but also back to your provider to get their opinion and evalution.