Coughing cat.

i have a indoor cat - about 10 years old...


she had been staying in our basement because she
is very timid and scared of the dog (beagle-poodle)
who would playfully chase her...


she is a long-hair brown tiger cat and i recently
(3 weeks ago) cut her fur short and she was quite
upset by this - understandably....

about a week later she began veturing out
of the basement and has been hanging out on
our first floor - out of reach of the dog.

(i also have been chiding the dog to not chase
her and he is learning)

Here's where the issue starts...

about a week ago - she began coughing whenever
she purrs - her purrs sound louder and
labored and if we
do not touch her - she doesn't purr - and there
fore coughs less - it sort of seems like the kind of heaves
they make when coughing up furballs?

i could not find much info about cats coughing...

my only thoughts were
1. that we have been running our
A/C in the hot weather

2. a couple months ago
both cats (her sister is a tuxedo and more demonstrative)
quit eating thier canned food - i would give them a half
can in the mornings and they would both usually have
some - they were slowly eating less and less of the canned
and finally almost none - i just thought they were getting
bored w/ it...?
( they also have IAMs dry food in a gravity feeder)

3. my mother has been recovering from a UTI and I saw
online that cats can get this - my mom is more of a dog
person - i have to tell her to pet the cats once in a while
...she does pet them but not much....
...the online comments said something about giving your cat
canned food to help them get over a UTI and that was when i
thought about giving her the canned food ( she was usually
the one who ate it mostly)

since she started coughing - i have been trying to give her
some can each night - (they prefer fish flavors....)
she has been eating it and seems a bit better but
the labored purrs and coughing / heaving seems about the
same....

any thoughts....?