If you are flinching so bad with the .44 that you miss deer then you'll miss them quicker with a 30-30...

Inside of 100 yards the deer will never know the difference...

Does the .44 have a scope on it??? If so, check the mounting screws and see if that helps...Also, try different brands of ammo as some usually shoot better than others...

After checking mounting screws on the scope, take it off and use the iron sights if the scope appears tight...