Just want to echo Al and Burair. I didn't have anemia, but it is common for a while after OHS.
Your heart has a lot of adjusting to do. You still have an Arnold Schwartznegger ventricle, and now it's doing Paris Hilton work. It will take up to six or seven months for the feedback systems that regulate your heartbeat to even that out. It's a complicated system.
Obviously, if things get painful, or if you have arrhythmias that don't go away within a couple of hours, you should consult your cardiologist.
The best things seem to be regular, moderate exercise (notably walking, which you should still be doing daily at this point) and time. You can walk just about as much as you want, although I wouldn't bring myself to exhaustion.
Wild or heavy aerobic exercise at four weeks is not likely to be beneficial to an arrhythmic issue, and may irritate the arrhythmias or cause other problems, such as with your sternum. Be cautious about your limits right now if you're visiting the dojo. The desire to be back to where you were may lure you to overdo for your current situation. Soon enough, you'll be able to get back to things.
Best wishes,