I second the opinion to get a second opinion. Any shop that will produce the actual data on paper/pdf before and after alignment is good with me, ask before you even drive there. And I’ve had tire shops balance tires +/- .5 oz. and ruin them in short order. BUT! You are probably at the time to do a suspension rebuild. Wheel bearings, control arms, etc. Anything that moves or is held in place by rubber. And even the best balanced tires don’t matter if they aren’t on a hub that runs true or torqued correctly. Most people don’t have this but for minimum $s the Harbor Fright, clamp-on, dial indicator WILL tell you if you have a wheel, disc, or hub wobble. Usually you can get the wheels off the ground and SAFELY put the car in drive just to watch for wobbles and listen for noise. Happy hunting!