Easier to get programmer or engineer jobs with Physics/Math BS?

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I graduated with BS degrees in Physics and Applied Math and I then enrolled in a Physics PhD program. However, I took a leave of absence and am now looking for jobs

I think I've only gotten a couple interviews for engineering positions, which were computer engineering/EE-related, but it seemed to involved lots of hands-on work, which I really hate since I always did poorly in my physics lab courses. For example, I hate doing the stuff that mechanics, machinists, and welders do

Anyway, I'm trying to figure out how to apply for jobs. I am obviously not a typical applicant for engineering or programming jobs. I've took a few mechE courses in undergrad, in heat transfer and fluid mechanics. Should I just forget about trying to get mechE-related jobs involving modeling/simulation (such as FEA, CFD)?

As for programming, I've been self-studying data structures/algorithms, learning about web development like javascript, and practicing programming for the past few months. When I was in college, I naively assumed that it would be relatively easy to get programmer jobs with a BS in physics/math because I worked on a physics project using C++. But as I've now spent a lot of time studying programmer interview questions, it seems there's an endless amount of knowledge questions and technical problems I need to know. I was contacted by a recruiter at Google, but it seems like I'm so behind that it's pointless to even try. I can solve basic problems like reversing a string, implementing a linked list, or converting a sorted array into a binary tree. But I just learned about stacks/queues a few weeks ago

It's been much easier for me to get interviews immediately for programmer/developer jobs (at smaller companies) than other engineering positions. But I've always bombed the interviews by being unable to solve really basic problems or not having completed enough prior projects. I also haven't written code on large repositories with different code-bases

Am I applying for the wrong jobs? Do I need to spend maybe another year studying before I have a chance at programmer jobs? Do I have a better shot at engineering jobs (hopefully not involving hands-on work) than programmer jobs?
 
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