So I've recently done my first run and from what I have seen it usually takes 1-2 weeks, but it has been about 18 days. Is this normal or is there anything I can do to speed the process up? Thanks.

Mods are generally given up to three weeks to verify runs. You could check the mods’ profiles to see when they were last online, and if they haven’t been online in a while, you can message them on social media and remind them that you have a run pending.

Alright thanks. One hasn't been active for about 2 months and the other was active yesterday. So I may send one of them a message or hope the more active one moderates it soon.

That's probably the best chance you got. after all, moderating is a sort of volunteer job, but hey, that's why there are communites built around stuff like https://speedrun.com. 😉