I am currently a student pursuing bachelor in computer engineering and in addition to that, I work as a product designer. I wanted to confirm if this would affect my eligibility for the challenge.
Eligibility Query for Swift Student Challenge
It seems to be incompatible with the very first eligibility requirement:
To be eligible for the Challenge, you can not be employed full time as a developer
Get details here: https://developer.apple.com/swift-student-challenge/eligibility/
That may be a bit subtle difference, if you work in a development team (they say developer, not code writer).
But you may try to ask directly the question to support (contact us): https://developer.apple.com/contact/. Events category.