birth injury, cp and no asd here. it didn't stop me worrying about it though, and i had a huge tendency to pathologise her every behaviour. for about two years i was convinced she was on the spectrum.
she isn't.
she just has cp.
her asd-ish quirks were just a result of the brain injury, and have been de-sensitised away.
there are kids with birth injuries and no asd. there are kids with asd and textbook births. there are kids with birth trauma and asd, and there are kids with no birth trauma and no asd. impossible to predict, but very easy to torture yourself for years with no real reason. 
my birth trauma baby does not have asd. one of my non-birth trauma babies is nt, the other one of my non-birth trauma babies has un-dx as/add/adhd/odd/ quirks.
really, no link has been proven. it won't stop you worrying about it, but only time will tell. and step away from google!
google told me my child would not walk (well, to be fair, so did the docs). they were both wrong.
there may be a slightly higher risk due to the brain trauma, but i really wouldn't waste any energy worrying about it. whatever will be, will be, and all that.
oh, re the epilepsy thing - we were also told higher risk of epilepsy (dd2 had neonatal szs and was eventually weaned off meds. sz free since). a repeat mri at 4 and a debrief with the neuro who talked specifics about areas of damage etc, said the area normally associated with epilepsy was undamaged in dd2. no guarantees, but much lower risk of epilepsy than the generalised 'higher risk due to cp' stuff. prior to that (for four long years) we were all watching like a hawk for absences etc. and spotted lots of really worrying symptoms, all of which were figments of our imagination. 