Under Eye Hollows
There are several options for treating this area under the eye, a very common concern. Fillers, as you mentioned, are not permanent but if done well, can give a great result. The choice of filler is very important in this region. Additionally, fat transfer can give great results in the area, but caution should be taken in younger patients as weight fluctuations later in life can result in a very unnatural appearance. Lastly, lower lid blepharoplasty with can be used to reposition fat in certain patients. The best procedure depends on your anatomy, goals, and age.
Newer under eye fillers good choice
I'm not sure what filler you had under your eyes, but in my opinion it is worth trying a filler again with either Belotero or Restylane Silk. Both are smooth fillers and unlikely to leave bumps.