Do the citizens of other Caribbean Islands Hate/Grudge Jamaicans?

i am jamaican born. but i spend half my time in cayman.. parents in cayman... but i school in jam. i cant help to realise that there is some hatred/grudge against jamaicans here in cayman. its very obvious here in cayman because caymanians are very out of order. in that they are not afraid to insult, put down, dgrade ppl... (and you know most yaadie here to hustle a money so then haffi suck it up)

but also i have had some experiences in other countries for example barbados... i really got a cold shoulder from many ppl once they heard my accent.. and i guess figured my nationality. i was even stopped from entering a store once. :( its really horrible.

i also speak to some ppl from trini barbados etc and i get a rude vibes from them sometimes...

if anyone agrees or have the same experiences.. please share. why do you think this is so?
Additional Details
a friend of mine says that ppl from the Lesser antillies are afraid of us and says we are wicked so because we eat poison... i.e Ackee!! hehehehe i dunno how true this is but it is funny.

in my history class we discuss this.. and we see some historican issues. the fact that jamaica was the hottest thing back then, financially and in developement. first to be independent of the FWI. and the fact that jamaica wanted out. etc

we also talk about now... the fact that jamaica is the most popular caribbean island... the fact that ppl dont even know the accent different (americans etc) and auto think that a caribbean person is jamaican.
for eg. Jamaica and Caribbean restaurant. my teacher sed she saw a restaurant with a name similar to that.. as if jamaica isnt apart of the caribbean..

we discussed it in class and made a conclusion that there is some grudge because jamaica takes the identity of the whole caribbean.. to most foriegners who know little about it anyway (most of them)