1997 Chrysler LHS Coolant reservior

It has been awhile, you are still the best site on the web. I just bought a a 97 chry. Lhs 500. Everything seems "Jake" today was driving in city traffic. Heavy. Last night the pseudo gauge was not to middle. I heard fans come on. This morning I noticed needle a bit past middle and I did not hear fans come on. So I like a dumby am gonna add water.I did not try to cool off first. Cuz nothing avail. As I unscrewed the cap coolant hot and bubbling so right away slam her back on. Drove in mountains needle didn't go past middle. When I came back a few hrs later I put bout 1/2 gal water. She has been OK. Question engine dirt, dust all over. Can I wash stuff out of compartment @ car wash maybe fan relay dirty? Or you geniuses, serious guide me your advice I have followed always excellent. An idiot like me success every time.I'm broke maybe 2.00 on my card I will gladly give it up. Many thx