The strips do actually work, just not like a dentist's treatment - I've seen a noticeable difference after a couple months of using them consistently, but the results were gradual enough that I almost didn't notice until I looked back at old photos. Three weeks is genuinely too early to expect much; most people need 4-6 weeks minimum, and you're probably not going to get that dramatic movie-star white that makes you think "wow, this actually worked" - it's more like your teeth go from pretty yellow to just yellow, which doesn't feel like a win until you compare side by side.
If you're really not seeing anything after 4-6 weeks of daily use, then yeah, professional whitening is worth the money because the concentration of peroxide is way higher and they can actually customize the fit to your teeth, so the bleach isn't just sitting on the front surface like with strips.