what do I have and is it rare

got a 88 gt convertible was told it was a cobra don't know never had a fox body before options I know of is a 2.73 rear posi auto pretty strong for such a hwy gear gets like 19mpg city unsure on hwy haven't been on any trip yet it has electric windows cruise a/c had a eq in dash has 6 speakers rides really stiff has a cowl hood a big wing on rear and 4 lug cobra wheels 17inch I can post a pic on here if you tell me how to get it on a thread but would like to know what it is and well about what it is worht it has 114k actual miles interior is goos other than the speaker covers on doors are broke and ash tray door stays open no tears in top or seats nice paint silver with black stripes has a ground effects kit on it says gt under doors no emblems on car or in interior car was originally yellow I think and was red at one time as well any help or info would be great

For 1988 a total of 211,225 mustangs were built. GT's numbered 68,468. Gt convertibles numbered 18,174. It had a base price of $16,610. The Mustang spearheaded by the GT was so successful in 1987 and 1988 that Ford decide to continue this model through 1993.
No, it isn't rare. Many were built although few exist to this date. The Kelly blue book value is $2975 for a Mustang GT convertible in excellent condition.

Ford never produced a "Cobra" in 88, first year was 93. Some Canadian dealers added the "Cobra" badge as a dealer option back in the day. What you have is not really considered rare.