clog in kitchen sink and shower?

Hi, guys! First time posting.

I just re-plumbed (in part) the 1974 mobile home we're living in. I got the water turned back on today, after a few weeks of remodeling (long story).

Both the kitchen sink and bathtub faucets burst forth with mud/rust/dirt, and are now only dripping. The toilet is slowly filling the tank. I have excellent water pressure in the bathroom sink and from the cold washing machine hose. I haven't hooked up the hot water yet.

Here's my novice guess as to what happened: Since the trailer was on a city water system known for rust and deposits, I'm thinking that there was buildup in the metal pipes. Since the kitchen faucet and bathtub were the first to be turned on, they caught the brunt of the deposits being flushed from the pipes. Once they were clogged up, there was nothing more to clog up the other things. The shower kit, bathroom and kitchen faucets, and toilet workings are all brand new. Does this sound like what it could be? I took the aerators off of the kitchen and bathroom faucets before turning the water back on. The washer hose was the last thing I turned on (running it into the tub), and it blew out some dirt before it started running clear.

If that's my problem, do I solve it by buying yet another faucet and shower kit? Or can I somehow hook up an air compressor and blow things out?

PLEASE give me some ideas! Thanks! BESmith1270 at Gmail dot com

It sounds like the piping supplying your fixtures is old, rusty galvanized pipe; the kind of piping that should have been replaced thirty or more years
ago. A small disturbance in such piping can dislodge rust deposits and cause almost complete blockage almost anywhere. There is no fix. The piping
must be replaced. If it's the city's or the mobile home park's piping, notify them. If it's your piping, well, you'd best get busy.

You "clean out" the faucets, you do NOT replace them.