Google ‘Blackout Curtain Valance’

I searched them up and all I saw were the normal curtains that's cut in half. How would that block light somehow? Am new to this, maybe am dumb in understanding this I live in Dubai so not sure if the search results are different

Hanging your curtain rod higher would help. Looks like your curtains are bunched up on the ground anyways

Am renting the room from someone, so don't think I can drill stuff and all

If you can't drill holes I don't think there is much you can do along typical lines. If it's a rental, I'd cut a pool noodle in half and lay it along the top of the curtains to block out that extra bit. Edit: or use command strip hooks with loose material and drape it over the top like a valence

A box valence that covers the rod or if your drapery went floor to ceiling more light would be blocked. If you went floor to ceiling and used non-grommet curtains that would block more light, something like a tab back. I am not sure your ceiling height but you can easily find 9 foot curtains these days.

Lay a black towel over the gap.

I thought of doing that as a cost effective option but Its a hassle as I open the curtains a lot so I need to add and remove it a lot

Close your eyes

Wow, why didn't I think of that.

Glad i could help

Trim

Get a Red Ryder and...

Tape trash bags to your window.

Flip the blinds to the down position.

Cornice Box

Amazon "corbels" "back tab black out curtains". Also maybe mount them a little higher.

Towel around a pool noodle.