Let it rest to relieve the swelling. afterwards, and I cannot emphasize this enough, you need to STRETCH your triceps, chest, lats and biceps. Deep tissue massage or a few ART therapy sessions may also really help this problem from coming back. Tendonitis or mostly any other "itis" for that matter is a repetitve stress problem stemming from altered joint kinematics. the joints get altered into a less than optimal movement patter from strength and flexibility discrepancies in the two opposing muscles that exert an effect on the joint.
It may be very slight but it is liken to water dripping on stone, let it drip long enough and the stone WILL erode.
The key is to keep the body very balance between the antagonistic muscles through flexibility, proper form, proper balanced training and strong proprioceptive development.
good luck my friend
oh and try this while you are rehabbing the elbow during your heavier sets. Best neoprene brance i know of(tommy Kono elbow sleeves are amazing)
http://www.prowriststraps.com/inc/sdetail/48705