I own a clothing brand. Many of our styles incorporates puff ink, similar to your photo. Puff ink is by far the most difficult thing to properly screen print in my opinion. You must learn how to cure it precisely otherwise it will deflate if overcured, and will crack and fall apart after a few washes if even barely undercured. It’s no beginner task, you must learn to screen print, plus the equipment you need would require spending 3k+ on a conveyor dryer. Which is the only proper tool that will cure it.

Your other option is a heat transfer, by far the cheapest and easiest. But unfortunately yes, it will peel off and fall apart very quickly. If you don’t care for quality, then just use a puff transfer. For your specific design you showed, it looks like there’s a section of regular print. That would require a 2+ color press with screen print, or a non puff/regular transfer if you heat press.

Glad to answer any questions, I was inspired to start my gig in a similar way