Forward SMS from mobile to iPad?

Hello, I have the following problem: My phone is broken, meaning the screen no longer works. Since I'm currently on vacation and unfortunately there's no one around who can fix it, I'll just have to deal with it for now. Luckily, I have an iPad with me, which also has my phone's Apple ID.

I recently wanted to log into my Instagram account, but I realized I'd forgotten my password. So, I first tried to do it via email. However, I got an error message saying there was no account with that email address. So I tried using my username and phone number. Which brings us to the real problem:

When I typed in my number and clicked "Send," I received the message "We've sent you a link via SMS to 49 *** ******* that will give you access to your account again." However, when I opened the SMS app, there was no sign of such a message. Now I strongly suspect that the message was sent to my phone and not my iPad. Which seems pretty absurd to me, since the SMS accounts are linked via the Apple ID.

So if anyone knows how I can access this email or how I can redirect it, I would be very grateful for that information.