I have the exact same thing, clear mucus in my throat that I cannot get rid of. I also have been doing the sinus rinses but I'm not sure if it did anything. I had mild case of cold/flu (not sure if it was COVID) back in November. Ever since then, I developed a cough for about 1.5 months from the post nasal drip. The coughing stopped but the nasal drip has not. I tried Flonase which helps alot but makes my nose ache a bit after continued use. My doctor also prescribed Ipratropium Bromide nasal spray which provided some relief but didn't cure it.
One of my friends said he has a post nasal drip too and he said Sudafed really helps so I got a package from my local grocery store. And he was right. I've been taking one 10 mg tablet once a day and I hardly even notice the nasal drip. The package I got (over the counter) is called Maximum Strength, Sinus Congestion, Phenylephrine HCL 10 mg Nasal Decongestant, Non-Drowsy. It contains 72 tablets. This works better than the Flonase (at least for me). Comes in a red/white package made by Kroger. It's cheaper than Flonase.