Considering that you wrote "these two things" instead of capacitors, I take it that you are not accustomed to doing electronics repairs, but this thought supplemented by your mentioning an electronics repair place.
As others mentioned, it is probably not worth paying someone else to repair, but there's more to it...
Those capacitors, due to the inherent design of a car head unit and their proximity ( lack of adjacent voltage boost circuit components, so almost certain to be the bulk power rail filter caps for the amp output stage) means they don't see a very hard life, combined with them not having domed tops, means they are probably fine, not the problem and that brown residue is just the adhesive they put on to help them resist road vibrations, adhesive which can turn dark from long term exposure to heat. That heat would eventually shorten their lifespan, but it would be a gradual degradation typically manifested by more distortion at very high volume, not what you're experiencing. If they had an internal short, they'd get so hot they would have spewed a lot of crusty electrolyte.
What damage is present depends on which two wires touched. I'd guess it is most likely that you touched a positive power input wire to a speaker output, and blew a transistor (or transistor inside an integrated amp IC). If that transistor or IC is now blown open, just it may need replaced. If it is shorted closed, not only it but upstream components in the power rail chain may have suffered overcurrent damage.
There are methods to use a multimeter to trace the circuit to find where power and audio signal are lost, to identify the fault. These seem like they may be too large a learning curve unless you want to take up electronics repair as a hobby which can be a very useful skill to have, but is not a short term solution to get the radio working again, and in the shorter term the value of your time will easily exceed the value of the radio.
I could be wrong about the value, some of those Sony units are pretty expensive. If you want that or another expensive unit to replace it, factor that in. I'd contact a repair place, tell them the wires shorted and there was smoke, and ask for a rough ballpark estimate. I would not mention the capacitors brown areas because as already stated, that is probably normal and not a sign of the problem. I'd take it to them, drop it off and ask for an estimate when they get to it (not while you're waiting at the counter) before the work is done, so you're not committed to an unknown bill. A professional will do that, but some repair guys are not so professional. Sometimes more is wrong and the bill is higher, but at least you've got a foundation for expectations.