Should I wash my Uromastyx?

Yes soaking a lizard can help remove dead skin as can mineral oil. If he has skin from left over sheds he needs it removed straight away. Use warm water not hot to the touch, it shouldn't hurt him unless the skin has been their for a long time (in which case try the oil). If the pet store let this problem persist they may well not have looked after him well, so a vet trip would certainly be a good idea but only use a qualified reptile vet as a vet who is inexperienced can do more harm than good. Ongoing his set-up should be correct to allow him to shed his skin unaided. Have you fully researched the care of this species of lizard?. Please read as much as you can on this animal and join a uromastyx specific forum for support as the species has very specific dietary, heating and lighting requirements. Good luck with your new pet, with the correct care he should bring you years of enjoyment.