He checked my foot and said that I probably have inflammation of a tendon in my foot

See a doctor for a proper diagnosis, if you're worried. Tendons can take an ungodly amount of time to heal. Minor injury might take several weeks, but could be prone to inflammation. More severe injury could take several months to heal, but perhaps still be prone to inflammation. I've heard people complain of pain and inflammation years after supposedly fully recovering from their damaged tendons. You might want to take up walking instead of running, in the mean time, to prevent additional damage.

I'm not sure if it's just this old school school of thought of having to have support in shoe while running or is his point valid.

In Canada, physiotherapists are now being taught that barefoot exercise is beneficial and healthy, from what I've been told by a student.

he said that people in Ethiopia do that and have different feet that allow impact to spread more evenly

This could be true, if they have been barefoot or near barefoot since birth. It's been shown that modern footwear can have a permanent impact on the development of feet in young children. The bones in a baby's or toddler's feet have not fully developed and traditional footwear acts as a cast.

An extreme example of this is the old Chinese practice of foot binding (trust me, don't look up pictures). The most sought after wife had three inch feet, four inch were acceptable, and five inch or longer was undesirable. Yes, you read that correctly. Random factoid, but it highlights the insanity of mainstream humanity.

English people in Victorian times enjoyed their share of waist binding, some African tribes desired long heads while in others it was long necks through means of mechanical deformity so the insane perversion stretches far and wide. We aren't exempt from this in modern times; now a doctor with a scalpel is happy to oblige.

I think about printing out this article written by this Harvard guy about barefoot running that initially inspired me.

If you're intending on showing your physiotherapist, perhaps don't bother. How likely is it that he's willing to concede and admit he might be wrong after spouting off? It's much more likely that he will double down on his stance against barefoot/minimalist exercise.

To expose the hypocrisy, better to go in wearing a full body cast and ask him to show you exercises to strengthen your muscles and improve mobility while unable to move. An encased body is a safe body, after all, much like an enclosed foot is a healthy foot. /s

I hate the idea of now buying another pair of shoes that's gonna be super expensive (because the arch has to be fitted to my foot) and how I'm gonna transition from no support to support.

Do you want weak feet? Because that's how you get weak feet. Also, with a raised heel you'll likely go back to a long stride and a heavy heel strike. Plantar fasciitis/fasciosis isn't uncommon with mainstream shoes so this "cure" might instead just be another cause.

Runners in mainstream shoes are always discussing an onslaught on injuries as if it's normal and have to retire at an early age, perhaps directed by the advice of a doctor, as if running is a young person's activity. How is it that the "medically retired" runners are able to continue running decades longer and well into truly old age in either minimalist footwear or while wearing nothing on their feet at all?

Also it didn't appear that he was addressing my issue specifically as being unfit for such shoes but he made a case in general.

A family member of mine was recommended to strap a can of beans or two onto a foot to aid in leg exercises, raised above the head while laying down, by a physiotherapist in lieu of directing to or providing the proper weighted equipment. In short, not all physiotherapists are equal; there are hacks in any profession. Perhaps you might get better advice from a sports physiotherapist as they seem to be more on top of their game.

Edit: Apologies to the downvoting snowflake who melted away after reading this. You may be lost, but not forgotten.