this problem can be solve with more practice and patient... but make sure you practise it correctly and light gauge and heavy pick helps.... get a good guitar book find out all the alternate, economic, sweep technique and learn
as for picks, Ibanez Sand Grip Heavy Picks would be a nice choice for you. practice every day and relax your wrist!
As a trick for alternate, just let your left hand follow what your right hand is doing (in the case you're not lefty). Start slowly and don't try to do it quicker if you cannot hear every note you are playing... yes i know its simple to say and difficult at the beginning but you will get impressed when you finally got it.