According to surf :

I didn't realize this was this complicated.

It isn't, really. Main problem is that we can't _see_ the
situation, and we have to grill you for details you didn't
think to include.

That unit was plugged into a different type of wall plug that has the
slits going horizontal instead of vertical.

That means the old unit was 240 volts (almost a 100% certainty).
You _cannot_ use the circuit for the new A/C as it is now. It'd
go boom!

You _could_ get the 240V circuit converted to 120V. It's
easy - many of us here could do it in 20 minutes for about
$1-3 in parts (a new receptacle).

However, given your apparent level of expertise, you should hire
someone to do this. It involves replacing the receptacle with a
standard 120V one, and making a slight change in the breaker panel.

If you can find a electrician _nearby_ willing to do this for
less than $150 or $200, I'd jump at the opportunity if I were you. Most
electricians wouldn't find a job that small worth their travel time.

Handymen would do it for less, but I'd be worried that they wouldn't
know anymore on how to do it than you...

If you have a _good_ DIY friend familiar with electrical work,
a case of beer might do it, but who knows how much they know?

She has been running it alot and it seemed to work OK except I guess it
trips every few days when it's not on. Iooked at the manual more
closely, it's says if the unit is more than 7.5 amps and 115 volts it
needs it's own circuit, but it's on the circuit with the small TV,
cordless phone, and bathroom. It says 11 amp/115 volts on the side of
the unit. If it remains this way, is there a possible serious problem
or what could happen ?

Very remote possibility. If the A/C cycles while she's using a hair
dryer, it should trip the breaker. Repeated trips may lead to a risk
of fire.

The breaker isn't tripping. It's remotely possible something else
on that circuit is triggering the GFCI, despite not being "downstream"
of the GFCI.

Converting that 240V circuit would give you the dedicated 120V circuit
you should have for the A/C and better isolate the GFCI from everything else.

This should be done whether or not the A/C turns out to be going bad
and needs to be replaced.
--
Chris Lewis, Una confibula non set est
It's not just anyone who gets a Starship Cruiser class named after them.