Am i allowed to submit a video recording that’s from a phone camera instead of a screen recording since I don’t have a capture card or is that considered unfair?

That’s completely fine. Several people, including I, don’t own a capture card and just use their phone to record.

There is no reason not to use a phone camera when you don't have a capture card. Just make sure to record the whole TV screen. (Even Th3on3C's All Games (NG) WR run is using a camera.)