"I wish I was" sounds correct, as it's the logical conjugation from "I am". However, for unreal or impossible situations, such as wishes and the 2nd & 3rd conditionals (which are unlikely/impossible situations), you always use "were". Eg. I wish I were richer... If he were a little smarter... You will find native speakers saying "I wish I was..." though it's not fully correct. No-one will beat you up for the mistake, but it is one of the indicators between "OK, passable English" and "good English".

Either can be correct. I wish I were a doctor. I wish I was a doctor. I wish I were fishing. I wish I was fishing.