Play the long game and just enjoy the movement, the climbing. Forgive me, but it comes across like you wanna climb to get buff. If my elbows felt the way you describe I'd forget the wall and go swimming.
I started bouldering last week, only done two sessions so far but planning on twice a week. Only issue is, combined with the gym 3 times a week thats like 3 sessions of pulling and 1 session of pushing, can see my elbows flaring up really quickly.. they've already started twinging and feeling weak whilst doing chins/bench . What do you guys reckon, carry on at the same volume and power through untill my body adapts to the workload (what i want to do because i enjoy it so much), or cut back to just one session a week and take it slower and ease my self in?