Does getting a new bike chain require getting a new cassete?

My chain was making a horrible noise and no amount of cleaning or lubing was making a difference. I finally caved and went to a shop and the mechanic who helped me said my chain was really stretched out and that I needed a new one. Then his manager said I also needed a new cassette, but they didn’t have one that matched my old one, and I didn’t want a smaller one, so I said, no thanks. Then I was hanging out with a mechanic friend last night and she said I probably didn’t need a new chain and I definitely don’t need a new cassette. I am having some shifting issues now (very difficult to get the chain in the center front chain ring but it eventually works), but the offending sound is gone although there is a NEW squeak. Obviously I need to go back to a different shop, but if anyone has any ideas about things I should ask about that would help. The guys I talked to yesterday were perplexed and kept thinking that the sound I was referring to was the chain hitting the derailleur which it wasn’t, it was a squeaky sound.

FYI the chain was a little over a year old. I ride 99% of days, and as of late probably average 80–100+ miles a week and lots of hills.