I live in a 6 year old house with a well. We have lived here for 2.5 years. Yesterday my cold water started sputtering. All sinks and showers, and toilets. It was really sputtering last night, but seems better this morning. (we were away for the weekend.) Is it possible to randomly get air in your tank?
How much further should I go with this?

Sounds like you lowered the water table and the pump's sucking air.
And this confirms it,
It was really sputtering last night, but seems better this morning. (we were away for the weekend.)
Your well replenished itself while you were gone. If this keeps on have the well checked by a professional. Good luck, Tom