I recently received an offer to work as an intern in UX/UI. I have a degree but it is not computer science related and was wondering if I would be able to get a full-time position following the internship (assuming they do not extend an offer) with another company, or if I will need to enter/complete a computer science degree. Most postings I see for jobs related to UI/UX have a minimum of 3 years experience required. Thank you in advance for your insights.
I've worked on design / ux teams where the people making the most UX decisions were design graduates. I personally built up industry experience and got into UX that way, without studying for a degree.
That said, can you get a job as a UX person straight after an internship? You might, if you have a great portfolio, and someone takes you on with a probation period. It's more likely to be a less specialised position at this stage of your professional development, though.
Based on my experience, I'd say you have a chance of getting a job that builds up your UX knowledge, but it will likely be more junior than being a dedicated UX person. You might find junior roles in design, testing or UI / front-end dev which can lead on to UX work. I started as a front-end dev.
There are many companies that will hire people who are fresh out of college for a full-time position as a designer. They're generally larger companies and they have teams of designers, and they expect that they'll have to help you grow your design skills, and they're willing to invest in that in the hopes that you'll have a long career with them.
A designer position will require a portfolio, so you should ensure that you can create a good portfolio about the design work that you have done (and will do during your internship). Your internship experience counts as experience, and should be a part of your portfolio.
You should also find local UX groups. You'll learn more about UX, and you'll have the opportunity to network and find out about open positions.
Depending on your financial situation, I'd say take the internship, and as soon as you feel good about your skill-set, start applying for jobs during the internship. Let your employer know about it if you feel that's possible without burning any bridges before you've crossed them, they might even make you an offer or give you a good reference.
Find a company that wants raw talent, and doesn't mind developing it. You might be lucky enough to stumble upon one that was set up by people like yourself, with no degree but plenty of talent.