I just went through a tire-balance nightmare with a tire shop (which I won't mention). I've been changing tires since I was in my teens and know my way around a balancer. I watched these guys make mistake after mistake. I was standing at the open bay doors coaching them. They had the largest weights on them both inside and out ..way too much! At the end of the day I put a stop to the process and took them to my local small-town Chevy dealer which as a brand new Hunter Road Force balancer ...and they know how to use it. A Road Force balancer has a spinning drum which puts up to 1500 lbs of pressure on the tire as it's determining the balance needed. That simulates road conditions and measures out-of-roundness and tire unevenness/vibration, etc. It can also help determine if there is a broken belt, etc. They (my Chevy garage) ONLY road-force balance's every tire they balance. They don't do it the 'cheap' way. And they also do rim-matching (rotating the tire on the rim to achieve the best balance). A lot of shops have R/F balancers but rarely use it ..or don't apply the complete road force features (because it's a time-consuming process). And if there's a lot of turn-over (a problem with tire shops) the techs likely aren't well-versed on how to use a R/F balancer properly.
Not only that, but the Hunter R/F balancer outputs a measurement of the final balance results, and it grades the degree of balance the tires are in. All GM garages (supposedly) do road force balancing my service mgr buddy was telling me.
It's a premium device and shops generally charge more than normal for performing full R/F balancing. In my case it was $75 to balance all 4 wheels and rim-match them. They were off the vehicle in the back of my pick-up. The results were going from like 6" weights the initial shop put on (inside AND outside), to weights which are about 1.5" (in and outside) in specific locations ...and they cut the balance factor (the Hunter R/F balancer measures in lbs) literally in HALF or more from what the original tire shop had them. And they run smooth as silk down the road! I've had other tires R/F balanced too in the past.
So the take-aways are:
1) tire shop guys don't always know what they're doing.
2) tire balancers need to be calibrated periodically (when was the last time the shop did that?)
3) Not all tire changers are created equal. Mosts don't use the premium balancers.
4) Tires can be out-of-round ...and a regular spin balancer won't flag a defective tire, or be able to compensate (balance) an out-of-round tire like a R/F balancer can.
In your case, given what you said, it could be a shock, and it bears looking into. But it could be too much air pressure, or even an out-of-round tire that wants to 'leap' when it hits a bump the 'wrong' way. It may make sense to seek out a better balancing job on a really good machine.