Hello, tiger. Yes, there's a difference between the two. If you are jealous of him, that means you wish your girlfriend was going somewhere with you instead of him. If this is the case, then you would use the third person "him". If you are jealous of her, you wish you were going somewhere with him instead of her. If this is the case, then you would use "me".

Neither 'him' nor 'me' would be appropriate here, she would simply say 'are you jealous?'. To be jealous of somebody means (effectively) that you would like to be them Here, clearly, the boyfriend doesn't wish to be the other guy. When a lover is described as being jealous, that means that he/she is possessive and is angry or afraid about their partner seeing other people: this is what she is accusing him of here, hence 'are you jealous?'.