This is going to be long as I believe that the context is important.
I have always been fairly good at maths and physics (won state wide prizes in the math contests and even won a gold medal in the national physics olympiad.) I live in USA/UK/AUS (trying to hide my identity).
However, after going through grade 12 I got a spot in medicine and happily went along with it because most of my friends were high achievers and I thought why not? I got a fair bit of recognition for getting into medicine (I admit I enjoyed the ego stroking) but luckily medical school is a graduate course (M.D), so I still had undergrad to go. I initially enrolled as a double major - math and physics but within the first week switched to a pre-med track as I thought that it would ease the transition into medicine.
Here's where things take a turn for the worse. By the end of second year I absolutely hate medicine and I realise that I truly do love maths and physics. I had luckily taken a couple of the first year mathematics modules - multivariate calculus and intro to linear algebra and two 2nd year course as well - intro to DEs and intro to probability.
So I talk to my course office and beg them to let me transfer into a mathematics track, but I am only able to do courses where I have the prerequisites satisfied and hence now (end of 3rd year) - have done, in addition to the courses mentioned above, courses on: nonlinear dynamics, intro to stochastic processes, a modelling course and a course on systems of coupled dynamical systems.
However, my true passion had always been physics and not only have I not done any meaningful university physics, but also haven't learnt a lot of mathematics - analysis, algebra and geometry.
I am thinking of going on to do a masters and try as hard as possible to steer myself back onto the path of physics and mathematics, but I haven't done a lot of the necessary coursework. Furthermore, my family is low income (another factor pushing me into medicine (no parental pressure) but the thought of a good income was tempting) and so I don't think I can afford to take a couple years to essentially redo a bachelor's degree.
My question is: am I screwed? I am more than willing, and passionate, to learn these subjects by myself - through books. In fact that's how I've learnt most of the things I have to date. But I realise that universities want to see another university giving a student their stamp of approval saying - this student has successfully learnt (insert subject.) I truly believe most of the time these stamps are meaningless, but in the case of admissions it truly is everything.
Please help, any advice is much appreciated.