Unable to login to new adobe account on photoshop - even after login in on Creative Cloud

A few months ago I downloaded a free trial of photoshop onto my MacBook Pro. I logged in with a personal email and had not set up any payment details to it either.

Today, I decided to go ahead a purchase the student monthly plan for all adobe apps ($21 pm.) I made this account through my individual university email - (completely different account and email to the one I made for the free trial). The payment has come out of my account, I have received a confirmation email as well as student verification. Now I have tried to log out of my own old account through the creative cloud app and into my new one, this worked. However I have re-opened up my photoshop app (after quitting) on my computer after login into my new account and it has still kept me logged into my old account, meaning I am not able to access my student plan.

How do I fix this?

Thank you in advance