The antibiotics would have been given to help her sores heal, without picking up infection. It would not stop or prevent itching. The steroids, antiinflammatories would have been to help the irritation. And although there is a long-lasting injection (usually holds for 4 months, if you are lucky) this isn't something I'd necessarily recommend for a puppy much as she's now older. Piraton, obviously, is good for an allergic reaction such as a wasp or bee sting - we keep some in the house always.
If you are in the UK, there are some lines (strangely more often in the bicolours than the tricolours, but that may still be down to genetics - those lines run within bicoloured hounds) which are more prone to skin problems than others. However, as good skin and coat comes from within, and with allergies, you should always look at the diet, I'd do just that. Cut out anything with cereals in it, at least starting with cereals as the first, main incredient. And there has in the past been some suggestion of overheating the blood via too much protein - the protein level in a dog approaching adulthood, would probably only need to be 26% maximum.
Malaseb, used to control malassezia, I've found, can do more harm than good, especially unless used quite diluted. Mine reacted with more red skin than before! There is aother produce called DermOpt, cheaper and off prescription, which seems to be milder.
Anyhow, by all means find a vet who specialises in skin conditions, but I'd also consider switching her onto a different food - suggest fish and potato. I use Arden Grange (UK) Sensitive. It's costly, but is gentle on the system (helped no end with my boy who had Giardia with lasting after-effects) and contains no cereal. You could make up a home-made fish and potato diet, using coley and mashed potato. AG Sensitive, which uses Hadock and potato, does contain all the supplements a dog needs, especially on that's still growing.
I hope you can sort this out because an itchy dog must be so miserable, to say nothing of it being irritating to live with one who is continually scratching