Usually, you should wait until you're late, so with 13 day LP, you should test 14DPO. But I'd give in at 11DPO probably
My LP is very short - 7-9 days only... so I'm trying to wait until I'm at least 9 DPO to test... tomorrow I'll be 8 DPO and I pray AF doesn't come!
You symptoms sound good, I wish you luck!