The crank arm on my fixed gear "slips" when I put large pressure on the pedals like when I take that first pedal to get the bike moving or pulling up hard on my toe straps to slow down. The slip is very smooth and feels like if your back wheel was spinning in place on wet tile/marble, however, my back wheel is not moving in situations when my crank arm slips. I've just gotten the bike from shop maintenance a few days ago too so I don't think it's an obvious issue? I've heard maybe I need it's a cog or lockring issue. Can someone tell me more? I need to be able to pedal forwards and backwards with a lot of torque safely. Thank you!!
Your lock ring is loose.
Normally the cog is quite tight from pedaling and you can do some braking with it. When you brake harder it breaks loose and unscrews until it hits the lock ring. This is what you feel as sliding. The lock ring has left hand thread to keep the cog from unscrewing completely. Now that the cog has tightened against lock ring, the process repeats when you pedal hard forward.
Now that the lock ring rattles loose, you should tighten it immediately.
The crank arms have to be really tight when they are first installed. Properly installed they last indefinitely. However, if they get loose and you ride it for a while the crank arm will be ruined. You can't fix it. Just get another one. An old used one is fine. You need a crank puller to get the old one off. They are not that expensive.