You can see if it says "2 year rule applies" on your stamp or on your DS-2019 form. If you don't see anything about this, then you probably don't have the 2 year rule on your J1, but sometiemes they mistakenly do not post this even though you do have the requirement. Best thing to do is to get an "advisory opinion" from DOS. Ask your visa provider or international office for help. If your support money comes from a US government agency most likely that you will have the rule.
2 year rule, prevents you from getting any immigrant visa. So you can still get non immigrant visas and work if possible, without fulfilling the requirement. I am not sure if you can get H1 if the rule applies to you, because H1 is both an immigrant and a non-immigrant visa...
Hope this helps.
