Yes. Look at your section scores and decide if worth retaking (i.e. somewhere you could easily improve), but your score is not low. A couple of those schools have average scores in the 90s and its comforting to be above the average, but that doesnt mean you dont have a shot with an 88.
From what I’ve heard, an SSAT score of 85% or above is acceptable to many top boarding schools because it shows them that you are capable of handling the of work they hand out to their students.
The SSAT is more of a critical thinking test so you should be proud of scoring so high on the test. Retake the test if you must, but scoring in the 88%ile wouldn’t take you out of the running in many boarding schools.
I’ve been told that Upper year is the worst year to apply. Lots of kids go to Exeter lower year. Approximately 1/3 of the graduating class, for the past few years, were filled with 3-year students.
You still have a great chance! Boarding schools aren’t specifically looking for one type of kid, such as the one who scores in the 98th percentile on the SSAT. They’re trying to make a group of kids that will all bring their different personalities to make a diverse student body. For top boarding schools, like Exeter, candidates are expected to score in the 85th percentile or higher, which you did!