New spider web after "showering" lemon tree? What to do from here?

For a few days now, I noticed that there are multiple thin webstrings around my potted lemon tree (its on my balcony). I read online that these could possibly come from spider mites. I couldnt really see any mites with the naked eye, but I saw these thin, singular webstrings that also seemed to get more as the days went by. And I think that my leaves also have some new damage on them (im not sure because I dont know which damage is new and which was already there). So yesterday, I decided to spray the leaves with some water to hopefully wash the mites and the webs off.I think it worked because there were some tiny white dots on the soil afterwards (though I still cant make them out to be mites). Anyways, I left the tree to dry over the night.This morning, I checked the tree again and to my surprise, the exact spot where I initially found the first web had a totally new and different web on it. It looked much more like a spider web with all those parallel lines you typically see and was way bigger than the few webstrings before. And I also saw a small orange spider in it.So now Im a bit confused...Why would this happen exactly after I shower the entire tree? Its my first time doing it and I am really confused...Should I shower it again or leave the tree alone? I dont want to kill the small spider in case its beneficial, but Im pretty sure that if I really have mites, just one shower with just water isnt enough to kill them.(Optional) 3. Am I blind or is it normal not to be able to see if that white dot is a spider mite? I even tried zooming in with my phone camera, but to no avail.