FHV-1 is endemic in the environment and impossible to avoid. We vaccinate against it but cats are exposed to the virus within hours of being born and so vaccination isn't completely protective.
Here's more in this regard:
FHV-1 is expected to go into remission unaided within 1-3 weeks. The bacteria Mycoplasma and Chlamydophila can be found concurrently with FHV-1 or as sole infecting agents but they, too, should go into remission unaided in that time frame. In the case in which my patient doesn't improve within the initial 10 days from the onset of symptoms, the antibiotic of choice - doxycycline - should be prescribed by Sesame's attending vet to address those bacteria.
Over the counter (not in all states) Terramycin ophthalmic ointment* is a good choice for addressing bacterial (not viral) conjunctivitis. Without time-consuming testing, we can't tell if a conjunctivitis is bacterial or viral and so presumptive use of that ointment is reasonable. Dosing is a 1/4" ribbon directly on to the cornea (clear window of the eye) thrice daily for a minimum of 10 consecutive days. Most often in very young kittens, FHV-1 can cause such damage to the cornea that it can rupture leading to loss of the eye.
Antibiotics don't address viruses such as FHV-1 but Sesame's vet can prescribe the systemic antiviral drug famciclovir if the vet thinks that a serious cause of FHV-1 is brewing. Antiviral ophthalmic products are also available.
As long as continues to eat, drink, and act normally in spite of the clinical signs of upper respiratory infection, and infected eyes don't worsen, Sesame doesn't need to be attended to by his vet. However, an inappetent cat will benefit from supplemental fluids given subcutaneously by their vet, a highly palatable and syringeable convalescent food can be prescribed, and you can purchase over the counter nasal saline drops in your local drug store to place in the upturned nostrils of a cat every few hours to help clear its nasal passages and breathe easier.
Please respond with additional questions and concerns if you wish.
If you can't find Terramycin ophthalmic ointment over the counter and a vet's attention isn't possible here's the next best choice:
https://vetericyn.com/product/vetericyn-plus-antimicrobial-ophthalmic-gel/ Discontinue its use if you see worsening rather than improvement.