the biggest thing i'd add is that cotton thread actually plays really nice with cotton fabric in ways polyester often doesn't. polyester can create friction issues on naturel fabrics, especially if your machine's been running for a while and the tension discs have any lint buildup. before you go swapping thread, try running a thin needle threader through those tension discs - sounds weird but lint gets trapped there and throws everything off. i've seen folks waste hours adjusting settings when the real problem was just dust.
one thing nobody's mentioning though: are you using the right needle size and type? a dull needle or one that's slightly bent will absolutely cause puckering, and a lot of people don't realize needles wear out faster than they think, especially on cotton. if you've been on this dress for a while use a fresh needle - they're cheap. also make sure it's inserted all the way up into the machine, because even being slightly loose creates tension issues that feel like they're coming from your dial settings.
the presser foot pressure thing is real (somebody mentioned it) but also check if you're pulling the fabric through. i know it's tempting to guide it but the feed dogs are doing the work - just let it flow. with cotton on a basic Singer you want medium tension, not loose and not tight. do a test seam on scrap cotton first, then adjust in small increments. if you're still getting puckers after a fresh needle and checking those tension discs, then yeah the polyester thread swap makes sense, but my money's on one of those first two things.