Novice question. Al told me to rest, but I really want to climb. Slap some sense in me. Mild finger soreness. Any advice?

I've been bouldering for 5 weeks now, 1-2x a week (more once than twice), 1-2hr sessions. Now a V3 climber but could send a couple V4s.

Early mistakes:

1. Due to my calisthenics background, I had always used my upper body to go up instead of using technique.
2. I repeatedly tried a V3 that had a crimpish start until I couldn't start anymore due to lack of grip/finger hold. This was the 2nd week I think. After this, I got a finger soreness that never fully recovered, though it's like 3/10 only now.

On my left hand, I have soreness on my A2 pulley ring finger. On both hands, the last joint (near tip) of my middle fingers. No soreness at rest, but 3/10 when pressure is applied.

Context:

• My recovery is mid, and I lift as well (mostly leg sessions).
• It's been 7 days since my last boulder sesh (intense 1hr).

Today, I want to do a volume sesh of v1-v2 only, but if I am advised otherwise I would not.

So, is it ok for me to climb or is it a must to ditch bouldering atm until my fingers are FULLY recovered?

I know I can climb, but I'm not sure whether I should back off and not take any risk or that this is just normal adaptation for beginners. As a new climber, I don't know a lot about finger situations. If I stop climbing now, I'll get my tooth extracted instead and take 2 more weeks off (3 total).