Yes, you can transfer, but it's more complicated than it seems. First, you need to pick a new university and find out if they accept outside students for your major - not all programs allow this. After that, you'll need: a transcript from your current university with all your grades, a certificate of enrollment from your current school, your secondary education diploma, your passport, and possibly a motivation letter. The requirements can vary, so definitely check the admissions office website of your target university - they usually have everything listed there.
As for course recognition - that's the most painful part. Each university has its own curriculum, and usually only general subjects like math or physics match up. The new university might credit your grades as pass marks, but they might also require you to retake exams or complete additional courses if their program has a completely different set of subjects. So there's a real chance you could lose a semester or even a year if the programs are very different. It's worth asking the admissions office in advance to roughly compare the curricula and understand exactly what they're willing to count.
A tip: start by talking to the dean of your current university - there might be a way to switch your major without a full transfer, just within the same university. It's faster and easier than leaving entirely.