It depends.
If Priest A refused to absolve you because you genuinely weren’t repentant of your sin, like you told him you planned to keep right on committing whatever sin you just confessed, then it’s pointless to go “priest shopping” trying to get one to absolve you. They’ll all say the same thing as Priest A, unless you lie to one of them or unless you find a priest who ignores church teaching.
Likewise, if you’re scrupulous and you go to Priest A regularly and for some reason he decides not to absolve you, or you start worrying he didn’t absolve you right because your scruples are interfering with your thoughts, then you shouldn’t go to another priest.
However, if Priest A didn’t absolve you because he misunderstood what you said, or got sick and passed out before he reached the point of giving absolution, or seemed confused and said the Memorare instead of the words of absolution, then it would be reasonable for you to go to another priest.