Same thing happened to me a few years back. Partially tore my left bicep. I tried to work through the pain but it became very painful. I had to take time off which is not my style at all. I went to a physical therapist for a couple months. They did the regular things like massage, ultrasound, ART, etc. I took nsaids almost every day for the first 3 weeks. Iced it a lot after my PT sessions and my own rehab sessions. You have to fight the inflammation.
Stretching it and doing high rep very light DB curls helped after I let it heal for about a month. The high rep bicep curls were probably the most beneficial things I did. I would take the 12 pound dumbbells and keep my wrist in a fixed suppinated proper curl position the entire time. I would curl them for 60+ reps. Sometimes I'd use the 10's for almost 100 reps strait. You get an absolutely insane pump going. This is rehabbing the area with extreme blood flow. Then after the set I would stretch them with a barbell behind me. That helps also along with helping the tendons. Look up DC bicep stretching. You hold the stretch for 1.5-2 minutes. It shouldn't necessarily be painful, but the pump should be extreme and give you that pump pain. It is painful, but you shouldn't be causing the type of pain that causes you to regress in the healing process.
Do the above at most every other day. Give yourself at least a day in between to heal. Do not go to failure on the curls, but get that extreme pump, then stretch, then ice, ice, ice.
To be clear do not do anything that hurts it. You will prolong your recovery by more than you would guess. I made this mistake.
Always ice it after you fuck with it. That's the key. You heat it, ice it. You massage it, ice it. You lift, ice it. You look at it wrong, ice it. Get it? You can't over ice unless you get frostbite. But that usually only happens to people that aren't healthy and have crappy blood flow.
Learning how to properly rehab, stretch and do mobility work has nearly kept me injury free the past 3 years. If I knew how to do all of this back then I wouldn't have partially torn my bicep like I did. The problem was it hurt and I kept working through the pain until it really hurt. Then too much damage was done and I needed time off.