Heavy vibration in my car after rough ride

I have a 2013 Toyota Corolla. I got distracted when driving and ran through a dirt center divide and got a flat tire.I had a replacement tire put on and after I started driving from the tow yard there was an immediate heavy vibration. There’s a big bump every time the car starts and when switches gears (I have an automatic) and in some gears the vibration is less intense, also when I turn the car at certain angles the vibration seems to go away completely but then returns when I began driving straight again. Can somebody give me an idea of what the problem is before I have a garage come and get for repair? Thanks in advance!

In addition to flattening the tire, it is obvious that you damaged some other components.
From a distance, nobody can tell you for sure, but some possibilities include…
a damaged CV joint…
a damaged wheel bearing…
and possibly even a punctured transmission pan.

Please do not drive the car any further, as more severe damage could occur if you do drive it.
The car needs to be towed to a reliable mechanic for assessment and repair.

Good luck…and please report back to us on what the mechanic finds.

you drove into a grassy median and got stuck? and damaged the wheel? you have a spare on now so i dont know if the tire was flat or if the wheel was bent/flat. maybe your spare is low on air? could have a bent suspension piece. control arm, tie rod, bent knuckle, damaged cv shaft, broken trans mount or motor mount. broken rack and pinion mount or rack itself. and so on

Sounds like a classic bad wheel bearing. Vibration that is lessened when you turn. When youre driving on a turn it shifts the weight off that bad bearing making it less noisy.

It’s the same rim as before, just a new replacement tire, right? Ask your shop to eliminate the new tire and/or the old rim as the cause of the vibration before assuming it is something else. They can for example put the car on the lift and turn the tire by hand and measure for any side to side wobbling or out of roundness. Likewise they can temporarily install another tire and rim and see if that one does the same thing. It’s also possible when doing all this, it won’t be the tire or the rim, but they’ll spot something else, the actual cause.

Is it a different rim? Did they balance the tire? It does seem something was damaged, but I would start with the tire and rim. Have the suspension checked.