Ignore the "second conditional"—it's not relevant here. In fact, this situation falls outside the n-conditional system, which is not a description English conditionals but a pedagogical device for teaching English conditionals. You've outgrown that system, and can now discard it.
The Condition Clause (protasis, if clause)
You say that you "don't know whether the dead mouse carried any diseases or not". That means that you're dealing with an 'open' conditional, not an unreal or counterfactual condition: you use a realis form ('indicative' if you prefer the indicative/subjunctive jargon). In the present tense you'd say "If the mouse carries any diseases..." But you're not concerned with the present state of the mouse (which is probably 'dead'!) but with its state at the time your car hit it, so you want to express the condition in the past tense with a past-form verb construction:
If the mouse carried any diseases ... or
If the mouse was carrying any diseases ...
The Consequence Clause (apodosis, then clause)
The form this takes depends on what exactly you're concerned with. If you want to express the event, the car's becoming infected, that's a past event, so you want to cast this in the past tense. Again, this is a realis situation, so the verbform elicited is a passive simple past: "... the car was infected."
It's more likely, however, that your concern is not with the event but with the car's current state—perhaps you want to decide whether you should have the car washed. If that is the case, you want a present form: either a simple present be + infected employed as an adjective, or a passive present perfect:
... the car is infected.
... the car has been infected.
