Sediment broken free in pipes has likely caused lower water pressure

Junk can also get trapped in the faucet valves too. You might want too ck the flow on the line that GOES TO a kitchen or bathroom faucet on the flex line that you can disconnect from the faucet. Try to narrow it down a bit. If you've eliminated all other possibilities and its affecting the whole house I would think the problem is fairly close to where the pipe comes in to the house, before the pipes start to split off. We've back flushed plumbing before with mixed results. Start at the point that's closest to the line coming in.
You want an open pipe outside for the stuff to run out. Not thru a spigot.I would try it before I started tearing everything up to replace pipes. Unless you have a crawl space. Good luck