Tension square query

[piemashandliquer]

I have just knitted my first tension square for hat Id like to knit. I've done a tension square as I've a tiny head and using Debbie Bliss Paloma alpaca which I think tends to stretch and I don't want it to end up too big. The pattern says gauge is 11.5 sts x16 rows over 10cm in stockinette worked in the round on 8mm. I did a larger than asked for square and within my 10cm square I have 13 sts and 18 rows. However I did them straight on a circular needle. I've got myself a bit confused and don't know whether I need to go up or down a needle size. Can anyone help please? Also, do I need to wash the tension square and measure again? I don't want to mess this up as the yarn was very expensive and I hav eRSI so don't wanr to have to re knit it if it's too big or small!

You are knitting slightly more tightly than the average.
If you have more stitches and more rows in the square then they must be smaller. If you wanted to make it bigger you would need to use a larger needle. Might it be better to continue on these needles though, to get the right size if your head is small?
Circular or straight, it shouldn't matter. You shouldn't need to wash the tension piece.
If you are using the correct yarn for the pattern they should allow for stretching.

Thank you Flossy, the pattern is not the specified one for this yarn, it is just one off ravelry for the same weight yarn. I will do as you suggest and stick with the 8mm as I do have a smaller head than average.