No, interest rate hikes significantly postdated the inflation. Fed started hiking in March 2022, and by that time annualized CPI inflation rate had reached 8 percent. Average over 2021 was 4.7 percent. In any case, interest rates increases are to combat inflation, they are not a cause of inflation
Moreover, wages did go up. US median personal income went from $35.8k in 2020 to $40.5k in 2022. Maybe it didn’t go up as much as other prices, but there’s nothing that says all prices have to rise by exactly the same amount during an inflationary episode.