The soapy water is there to make the tire easier to get on but also to make it seat on the rim uniformly. Break the bead from the rim on both sides, put some more soapy water on both mating surfaces of the rim and inflate and re seat the tire.
Do not slop a lot of soapy water or you could get some inside that would make the tire-wheel impossible to balance.
I doubt very seriously you have damaged anything, just reseat with soapy water on both sides and you should be golden.
If you still have a vibration have the appropriate tire-wheels balanced.
regards
mech
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