Agree with above, sounds like an earlier bedtime would help.
Sounds like my LO (also 13 weeks)😅 Does your baby sleep well during the day? My girl struggles with day naps so I figured she could just be really tired in the evening from being a really active baby the whole day. At 6-7pm when she becomes unsettled I usually put her in a sling and rock her to sleep (she eventually settles). Then she wakes up at around 8-9pm for a feed and straight to bed. And she sleeps until her next feed at around 1am x
This sounds just like my baby too. She’s 10 weeks and has a screaming episode most nights where she’s inconsolable. Only thing I’ve seen work so far is ‘Dancing Fruits’ on YouTube until she falls asleep. Someone had recommended some probiotic drops so going to try that out
When our bub was having his witching hour (which sounds like what you’re describing), we put his bedtime to earlier to try and prevent it - have you tried putting your little one to sleep around 7pm just before it normally starts? It worked for us - but it was when he was a few weeks younger.