welcome to the wonderful world of elbow tendonitis!!
Some of us are apparently genetically predisposed to suffer from it, yay! NOT! I struggled with this monster for years!
Back off the grades, at least until you have built a solid base level of fitness then work up them slowly. Develop open hand stregth so you dont crimp so much, vary the way you take holds as much as possible even if they are all jugs. Start stretching, especially your back and shoulders, its important to flush out old lactic acid so that the tiny overworked muscles in your forearms can recover.
Get the physio to give you shoulder stabilisation exercises and do them religiously, wirst curls can irrtate inflamed tendons, try wrist pronaters instead, they stabilise and strengthen the forearm without the tendons sliding backward and forward in their sheaths (as with wrist curls) which is what causes the irritation.
Once you are pain free and strong again it will still hurt on hard climbs, deal with it! Cranking hard routes freakin hurts period. Pain at first that disappears as you warm up is ok as are occasional dull pains during workouts, sharp pain or pain that builds and/or persists after a workout is not! If you are experiencing the latter you are not fixed yet. Go back to the physio (if you can go to one who is a climber you will be in the best hands) and listen to what they tell you to do! Good luck! Your symptoms sound mild, hope you get fixed before the pain radiates up your arm and across into the spine, and the elbow becomes inoperable and you cant lift a teacup!!