There are really [sorry] two questions here: (a) "I did get jealous" vs. "I got jealous", and once you have decided, (b) where to place "really". For (a), "I got jealous" is the neutral way to say it. "Did" is more often used in negative or interrogative contexts and typically used in affirmative contexts only to emphasize the point and in particular to contradict an assumption to the contrary. It is often marked in speech by a stress on "did": "So you didn't get jealous, then? Oh yes, I _did_ get get jealous, but I didn't show it." On (b), the adverb "really" can go either with the verb or the adjective. "Really jealous" means "very jealous". "I really got" or "I did really get" means "I definitely/certainly/absolutely became". Now for your example, it doesn't much matter to the sentiment which you use, but in some contexts it may make a difference.

In your examples, the difference is minimal, since "really" can serve the same purpose as the emphatic construction. The first one, using "did," implies a contrast with the negative sentence, whether stated, implied, or merely thought. Probably the speaker was of the opinion that the other person had not gotten jealous, so the did emphasizes the contrast.

"really did get ..." the anger is stronger than "relly got..."