Nissa,
Can you tell us what transmission style you have: standard or hydrostatic? Is the machine moving while changing the direction of travel? What tire wobbles, how much and in what direction (side to side or in the direction of travel)?
Just a thought: If yours is a standard (has gears) then I begin to wonder if the clutch is adjusted properly. This assumes the clutch peddle is being depressed while the gear selection is changed.
Peter