The answer to your question as to whether the pin hole can cause the engine to overheat is no.
I suspect from your description of squeezing the radiator hoses is that you are overdue for a change of hoses. You should not be able to squeeze good hoses like that.
Since you will be changing the hoses, why don't you just keep going, remove the water pump, remove the hood, undo the cowl to radiator brace at the front and one side then rotate the brace upward, undo the 6 bolts holding the radiator and remove it. Take it to a radiator shop to get it repaired and cleaned out. Flush the engine block. Do a tune up. Put everything back together with a thermostat and you will be good to go.
I drive my stock '51 pickup with a 216 in 115 plus degrees in the Phoenix area with no problem at all.
You can do it! And you will be glad you did.
Kent