Do I need a wheel alignment when changing your old rims and tires for a new ones?

Balance the tires

Sounds like wheel balance, check front wheels for loss of weights outter and inner rim, alloy wheels have sticky weights steel rims have clamp on weights either can be lost....say if you clip the kerb/sidewalk or just through centrifugal force. A garage will check wheel balance and attach weights if needed.

sounds like a bent wheel or a separated tire. should be pretty easy to spot by spinning the tires by hand.

I’m happy to assist further over the phone at https://www.6ya.com/expert/jeremy_d728a59f986299fa

If they have been spin balanced properly, then the wheels and/or tires are out of round or you have a bent rim. The right way to check this is to use a dial indicator and measure the runout of the tire and the rim. A good tire shop should have the equipment to measure this. There is always some radial runout (difference in distance between the center of rotation and the outer surface, both on the tire and on the wheel). When the tires are mounted on the rims, If the high spots of the tires happen to be aligned with the high spots of the rims, this makes the total runout worse. If the high spots of the tires are aligned with the low spots of the rims, the total runout is better. There is a limit on how much runout is acceptable to give a smooth ride. The tire shop should also measure lateral runout, which is the side-to-side variation in the wheel as it spins, or "wobble". If excessive, this would be a sign of a bent rim. Also, with the vehicle jacked up so the weight is off the wheels, you should check for any looseness in the suspension and bearings, which can also cause vibration.

Camber and caster settings are off. Have 4 wheel alignment done by a good shop and save your nice tires. Out of alignment will make steering feel heavy and wear tires fast!

Your Checklist

The alignment was poorly done
You need new brake calipers, the right one could not be letting go
Get the Rims Checked they could be bent
Did you also align the rear wheels
Tires - Condition / Quality
Bent Rims
The new tires you purchased.....are you sure they were first grade and not second grade tires?

I would check your front tires for any defects if there is none noticeable I would get a front end alignment. Most of the time you can tell if you need a alignment if your car pulls to either the right or left while driving. Hope this helps.

First we need to know where is the shaking noise coming from?Is your car a 4X4?If noise comes from a driven wheel it can be the differential system or bearing also.Usually the speed you have specified is pointing to wheel alignment problem.Also can advice to go to a different tire shop and check wheel alignment again,also ask the mechanic to check the state of your wheels and tires.One of them may be damaged .

it could be as easy as checking to see if you have a dented rim.....

or as expensive as changing the "constant velocity joints" but only if it is a front wheel driven car.....

how are your shocks?

have they repacked the rear bearings..."but only if not rear wheel driven car"

Have you tried cross checking with another wheel alignment specialist? To me it seems to be coming from the tyres or a dented rim. You could ask them if they do dynamic wheel balancing on the car itself. This will take in consideration the out of round of the hub as well.
Let us know if there is any change.
Cheers.