hey there Aylin!
welcome to Amman, yep there's alot of great hairdressers and good saloons in town, my favorite is Toni&Guy it's located inside Grand Hayyat Amman Hotel at the 3rd Circle , here's their website:
and here's their phone number 06 4622 463
here U can check many other good Saloons in Amman through this website and many other stuff,
p.s you're most that welcome to text me in private 