front and side planks, one legged and 2 legged are an excellent all around core exercise that just take floor space occupied by your body. Also V ups, long slow controlled curls up and down with feet just slightly off the floor. Pushups, modified but preferably full body are good as well

good luck with that, as for lossening up, shoulder rolls front and back, arm swings and head and neck rolls ususally feel pretty good.

marni