First, the antibiotic shot. Unless it was convenia, which lasts for 14 days in the body, any other shot was pointless. But! Even if it was convenia, that is not a great antibiotic choice for a upper respiratory infection.
Hving had chronic respiratory issues, I would make a very good bet that there is likely a primary underlying viral condition (especially herpesvirus), which is predisposing to all these respiratory problems.
Nonetheless, you still need to get the respiratory infection under control and get appropriate eye medication as well.
So, you need to get back in to the vet or select another vet for a second opinion.
For recurrent respiratory infections, very good antibiotic choices tend to be either doxcycyline (never in tablet form for a cat. Always the liquid). Or zithromax. Yes, we use zithromax in cats as well.
Also, for the high suspicion for a underlying herpesvirus, I would definitely ask your vet for a lysine supplement like Viralys or Enisyl. It can help over time.
Hope that information helps