Bassett's are notorious for having persistently red eyes due to the exposure of their conjunctiva to air due to the drooping of the lower eyelids.
Her eyes may not be so much "infected" as they are inflamed with excess mucus production ( vs. pus).
What is going to be important to determine is if your girl is producing enough tear film to lubricate and coat her eyes. Bassetts can develop a condition called KCS or Keratoconjuncitivitis Sicca where they have poor tear film production resulting in chronically red, dry, mucus laden eyes that are painful and eventually can develop permanent corneal scarring and subsequent visual impairments.
In addition, Bassetts are NOTORIOUS for developing Glaucoma or elevated intraocular pressures that can manifest as inflamed/red or painful eyes.
When you go to the vet's tomorrow they should do several things to complete a proper ophthalmic exam.
First, a schirmer tear test should be done to measure your pet's ability to manufacture tears in both eyes.
Second, a corneal stain using Fluorescin Eye Stain will be used to visualize any defects or ulcers on your pet's cornea(s).
Next, a topical eye anesthetic, will be instilled onto your pets eyes, and then a measuring device called a Tonopen will be used to measure the intraocular pressure in each of your pet's eyes.
The findings of each of these tests should give your vet a great idea of exactly what is causing your pet's eyes to be abnormal! Based on these findings, your vet can prescribe specific medications or treatment protocols to help reduce the symptoms of your pet's problem.
If your vet does not have the capacity to perform these simple tests in their facility, than I HIGHLY recommend referral to a practice with the capabilities to do these tests, or to a board certified ophthalmologist in your area.
Glaucoma must be diagnosed early to prevent retinal detachments and permanent blindness.
Corneal ulcers are painful and need early diagnoses to help speed healing.
KCS is a serious disease that will require lifelong therapy in most cases.
The best case scenario is that your Bassett just has red, irritated eyes from Droopy Lid Syndrome!! I gave you all the possibilities just so you could mentally be prepared for different scenarios!
Let me know how the vet visit went!!
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Best wishes to your and your pet, Dr. Smith