My iPhone is showing me no service for some days now

Just out of the blue?

Try this:

Remove and reinsert the SIM card.

If it doesn't help contact your carrier, maybe the SIM card is damaged, ask for a replaced (new) card. Normally it is free.

Also  ask to check if the SIM tray is bent, as even a tiny misalignment can cause the SIM card to not fully connect with the internal contacts in your iPhone.

If it doesn't help, see these Apple articles below:

If you see No Service, Searching, or SOS on your iPhone or iPad

If you see No Service, Searching, or SOS on your iPhone or iPad - Apple Support

Manually update your carrier settings on your iPhone or iPad

Manually update your carrier settings on your iPhone or iPad - Apple Support

Update your network provider settings manually on your iPhone or iPad

Update your network provider settings manually on your iPhone or iPad – Apple Support (UK)