Milo was on Baytril for another infection and her owner saw the affect it had on her appetite which is why she requested a different antibiotic. If the Baytril was a more appropriate course than the Terrimycin then the vet should have said something. The owner's request was made in order to prevent Milo from losing his appetite not out of convenience for the owner.
URI's can turn into a pneumonia in a heartbeat, and Terramycin is not generally as effective for treating a respiratory infection, any more than Sulfa is (though I prefer sulfa over Baytril if I can possibly use it). Milo seems to have an awful lot of health problems going on with one little chin, more than I've ever seen in any one else's. I agree with Julie. You have to wonder if there is something going on that just isn't getting cleared up. Maybe the antibiotics were not dosed correctly, not given long enough, etc., and now there is an infection going on that needs cleared up for Milo to be healthy.
I personally would not use anything other than Baytril for a chin with a URI, regardless of whether it puts them off their appetite. It's an inconvience for the owner to have to hand feed, but that is not a reason to go with a lesser antibiotic buried in sugar. If you have an already sick chin, their immune system is down, they are not eating well already, then you slam their system with a bunch of sugar 3 times a day for however long? That is not going to do anything to help their appetite or to keep their gut flora normalized.
Also, do I remember right that your mom is/was a vet tech? (Could be thinking of someone else.) You could eliminate the problem of inappetance by administering the Baytril via injection rather than orally. I personally have no problem administering it orally. I simply give a "chaser" afterwards, i.e., a rosehip, a piece of a bite sized shredded wheat, a few rolled oats, a bit of critical care - just somethign to wash the bad taste away.
ETA: If she's not eating at all, 60 mL will not even help her to maintain weight. You're going to have to go up from that, get her to level out (which you won't know what level is unless you get a gram scale and not a pound scale), and then you can keep her at that amount for maintenance until she's eating on her own.