Maybe it would help if you gave us some concrete examples of concepts or methods that you felt you were just being forced to accept and memorize, rather than being provided with the underlying rationale for them?
There is definitely some physics involved. Kirchoff's Voltage Law (KVL, also known as the loop rule) is basically just the conservation of energy. It says that the sum of the potential differences around a closed loop in a circuit is zero. Charges can't have a net gain or loss of potential energy around a loop, else energy would not be conserved.
Kirchoff's Current Law (KCL, also known as the junction rule) says that the sum of currents going into a junction (or node) is zero. In other words, the total current entering the node must be equal to the total current leaving the node. This is just an expression of the conservation of charge. If more charge were entering a node than leaving it, then charges would have to be disappearing into thin air. Similarly, if more charge were leaving a node than entering it, then charges would have to be magically created out of thin air.
Both KVL and KCL are limiting approximations to what Maxwell's equations say would happen. The approximations are valid when certain conditions are met.
Ohm's law shouldn't be taken as a strict "law", but rather a result that has been shown experimentally to be true (or approximately true) for some devices/materials.
Perhaps you have trouble with socalled "idealized" circuit components such as an "ideal current source" that outputs a constant current no matter what? These are not meant to correspond to any sort of realistic devices or components. They obey the rules that they do simply because we stipulate that they do so. (In other words, they obey those rules by definition). They are useful pedagogically in order to learn circuit theory without overly complicating things by having to adopt a more realistic model for the behaviour of a device. That comes later.
If you wanted to implement a constant current source or a constant voltage source in real life, it would be nontrivial and require some active electronics, not just passive components.
That's what I can think of off the top of my head.
EDIT: Also, sign conventions can take a bit of getting used to. But they are just that: conventions. We assume a polarity for the voltage across a resistor in a circuit, and then we assume that the current flows across the resistor in the direction from high potential to low. If we then get a "negative" current as an answer from doing our circuit analysis, all it means is that the actual direction of the current across the resistor (and indeed the voltage across the resistor) was in the opposite direction from what was assumed.
