Lil everything crossed for you 
Welcome Brooke! As far as I'm aware you go by lmp until 12 wk scan as earlier scans can be more inaccurate (certainly how it worked out for me, though mine was at 8ish weeks for suspected ectopic). Regardless, 13w is fine for 12w scan, the limit for nuchal measurement is 14w.
Unsurprisingly I have a banging headache in the heat despite drinking an ocean of water. Really need to discuss with midwife at next appointment, they're not fun! Hope everyone else is faring better, cooler tomorrow hurray!