There are a number of techniques available to reshape and build up the bridge of the nose during Asian rhinoplasty. Synthetic implants such as silicone implants carry a higher risk of complications (including infection, migration, and extrusion) than grafts made from your own tissue (autologous grafts). In general they produce aesthetic results which appear less natural than an expertly placed autologous graft, and do not produce a permanent result.
Be sure to understand the advantages and disadvantages of the available techniques in order to make an informed decision.
Infection of silicone implants are always possible. This is not a botched surgery but rather a known complication of silicone implants. Your nose can be reconstructed with cartilage and fascia so you do not have this problem again. See a very experienced revision rhinoplasty specialist for correction.
There are risks and benefits to every procedure. Infection and extrusion is a risk in augmentation rhinoplasty and usually these risks are discussed preoperatively. Once the infection has settled down, you may benefit from revision surgery. Your best recourse would be an in person evaluation with a board certified facial plastic surgeon with expertise in Asian rhinoplasty.