How to keep a block wall from blowing out at the bottom
Blocks are very strong under compression from above, so if the walls are bowing under the weight of each course of blocks, that makes me think the walls are not plumb. You would need to tear down the walls and redo them to be plumb.

You say you want your walls to "withstand the pressure of the dirt." Are you burying the structure? Correctly-built block walls may be strong under compression, but they are weaker under pressure from the side. Tread very carefully. It sounds like you may want to involve the services of a masonry professional if you're not sure how to build a block wall in such a manner as to prevent it from collapsing under whatever loads you're putting it under. Built correctly, block walls are very strong. These blocks are resting on a concrete foundation, right? Ideally you would have a concrete foundation with rebar sticking out of it that you would place the blocks over such that the rebar goes through their cores, and then you would grout or concrete the cores to tie the blocks into the foundation. Block walls are very heavy. Without an adequate foundation, the structure is doomed from the start.

If your block walls are not straight, plumb, and tied into an adequate foundation, you'll need to redo them so that they are--end of story. If all of that is fine, there are a couple of ways you can reinforce your block walls to increase their resistance to exterior pressure from a bunch of dirt:


Put rebar through the cores and pour concrete in them.
Apply a layer of surface-bonding cement to both sides of the wall.


Do both, and the wall will probably outlast your great-grandchildren.

But again, I would strongly recommend hiring a professional to help you. You don't want to build a structure that's unsafe. Masonry is heavy. If it collapses when someone's inside it, that person is probably a goner.