I'm sorry to hear your little one is so unwell.
Is the discharge coming from her back vent nearest the tail (anus) or her front vent? If it is coming from the further forward one it does sound like she may have a pyometra which is a very serious infection of the womb. The womb fills with pus and it can discharge a foul smelling fluid.
Antibiotics won't cure a pyo I'm afraid. It can affect hamsters of any age. The only cure is to have her spayed - removing the intact womb and infection which can lead to a good recovery and a long life afterwards.
The antibiotics may give her some remission but the infection always returns much worse eventually.
If she is in good heath otherwise this is the time to do it as she is young and likely quite strong still. The vet should be able to do a scan first to establish if there is pus in the womb then proceed with the spay. Costs vary but on average you are looking at maybe £120 to spay her. I'd try and find a vet who has experience of this. Where abouts are you located generally?
Other things it could be but are less likely given the symptoms are a bladder infection, tumour in the bowel or an ovarian cyst which may be causing hormonal issues. Cysts can be removed. Tumours are often entwined in the bowel and not removable sadly. I'd see the vet again with these thoughts and ask for a scan.
There is some good info here:
Vectis Hamstery and Exotics - Pyometra in Hamsters
Hope you can get some help from your vet and she makes a good recovery x