It's probably not the shoes. That would be almost last on my list of potential causes.
First, it's highly likely that you incurred an overuse injury, by jumping from zero to 50 miles to 100 miles in a very short span. You shouldn't increase your riding more than 10% per week total.
Second, it could be any combination of improper fit and technique that contributed to your problems. Your saddle could be too high, too low, too far forward or too far back. Also, you might have too low a cadence, particularly on the hills. You want to spin rapidly and with minimal force at all times, even on the hills.
Third, if you have arch issues you should use whatever inserts you normally use in your cycling shoes as well.
Fourth, there is some recent indication that a high degree of float can actually aggravate knee issues. However, the studies are still a bit preliminary.
That said, it seems unlikely that other than float, the type of clips you use won't affect your knees. Bigger clips will give you a stronger grip (which you really only need if you're sprinting) and can relieve some "hot's foot" sensations.
I'd get some rest and a proper bike fit first, then proceed with a more rational training regime.