It sounds very much like some sort of
noise reduction/gating/expansion is "taking out" most of the noise, which is why you only hear it when you speak. It is there on the source the whole time actually.
See if you temporarily can disable that noise reduction effect whereever it is. This will allow you to identify the noise origin and do something about it.
The issue could be related to one or more of these points:
- the room has reflective surfaces (tiles etc)
- you used some badly isolated headphones
- you didn't use headphones and had monitoring on with external speakers or laptop speakers
About #1: get some carpets, curtains etc things that dampen the room, and if you do not already use a microphone reflection filter get one.
About #2: You'd be surprised how much head phones can leak, and how well high gained large diaphram mics will pick that up ;-) Combine that with #1 and its bad. Get a decent set of closed back on ear headphones and keep the volume down.
About #3: This should be obvious: having your own voice monitored as you speak will create echoes, feedbacks etc, because it gets picked up again by the mic. Combine that with #1 and it gets really really bad ;-) Don't do it, get decent headphones.