Should I play rapid to become good at blitz?

I'm not a beginner, I'm not very good either, I consider myself ok, rn I have like 17+ elo on rapid, and (even though I play a lot of blitz) I'm STUCK at 14+ elo on blitz (3+2) on 3+0 I'm even worse cuz I think too much and get a winning position but then I lose on time, or I try playing fast to have time advantage and blunder everything 3+0 sucks for me 😣 although I would like to become good at 3+0 too... but it doesn't matter, the point is, how can I improve my 3+2 skills? I study stuff, I make puzzles etc, but it's not enough, should I just stop playing blitz and play full rapid instead? and then naturally I'll become better at blitz by improving in rapid? Is rapid the way to go?