There are a number of issues with your sentence.
A rephrased suggestion would be:
We were standing close to the kitchen sink when this
lady came and opened the tap, which splashed water all over
- Spelling correction on clothes (instead of cloths)
- You can use sprayed instead of splashed
- If "this lady" is named then using her name would likely be more appropriate
- If you would like to use the word sprinkle then you should use it more as a verb than a noun (IE "...the water sprinkled onto Mike's clothes...")