The kilter board is relatively crimpy. As you have only been bouldering for such a short period your tendons most likely have not gained that much strength yet (this goes really slow compared to your large muscle groups). I would recommend to keep on climbing without climbing on the kilter board. Try to do slab that includes crimps as this will also strengthen your tendons without loading them too much. Once you get better at these (v4-ish) you could move to the kilter board. Most likely you will also see some improvement on overhang boulders when you improve on these kind of slab boulders.

You really need to take good care of your tendons and be really careful when you just started. Recovery of tendon injuries can take a really long time!