These readings are exceptions, sorry! Here's a mnemonic to help you:
When someone asks you who gave you a souvenir, just say "Miya gave (みやげ) it to me." Who's Miya? No idea. But neither do they. You never have to remember who gave you anything ever again! Miya gave you everything you own. She's probably a great person.
I haven’t picked out a souvenir yet.