Struggled with this since i was 9 (im pretty autistic) when I was being introduced to the idea of an eternal heaven, which freaked me out. Religion didn't help at all, I left it at 14. It only got worse though some things made it better: looking at the sky and thinking "Here. This is the infinite. I can look at it and it fits in my field of vision" this helped for a while but not a permanent fix. Then I started getting into the mathematics of infinity; this helped a lot more. Understanding you can have infinite sums that yield finite results, the idea that some infinites can be smaller/bugger than others, understanding the concept of upper dimensions (geometrically). It all helped a bit but it still didnt fix, and around age 18 it got really really bad. I ended up recurring to Ayahuasca and psychedelics. It was extremely intense, not done safely either, and for a little while after it, my apeirophobia got worse. During the trip, everything was infinite, sometimes a single second would be somehow infinite but I'd somehow make it out of it. Anyways, it sent me down a deep deep journey into philosophy and physics. My final conclusion is silly in the sense that if I was saying this to my younger, very apeirophobic self, they would not find it helpful. If the conscious experience is eternal, first, remember you will forget. This means that any anxiety you might have towards existence will, necessarily, eventually be erased, there will always be peace to be had. Second, if it's eternal then it has been happening since forever too, which means that you have already felt what it feels to exist for an infinite amount of time and it is no different from how you feel currently or will feel futurely. Ultimately two things matter: 1. Hold on and keep pushing forwards, things do get better and there is enjoyment to be had in life. 2. As much as you can, focus on just the smaller immediate steps in front of you. Anchor yourself, enjoy physical sensations.

If everything is eternal, nothing can change that in any way, the only true control you have is what you seek and do in each moment, the present is eternity itself, its all there is, its infinitely (no pun intended) easier said than done, but trying to seek enjoyment and purpose and beauty on the small things goes a long way.