Hello matcheee
The pressure is going up because the gas pressure inside the bubbles is larger than the gas pressure outside them. Picture a bubble with a continuous film of liquid around it. Consider a plane passing exactly through the middle of the bubble. The force pulling the two halves of the bubble together is the perimeter length of the bubble multiplied by the surface tension of the liquid, force per unit length. Times two I think because there is an inner and an outer surface. To keep the bubble from collapsing, that tension is opposed by the air pressure inside the bubble, so that the opposing force is delta-p times the area of the circle described by the plane passing through the bubble.
Then, 4*pi*r*(surfacetension) = pi*r^2* deltaP
and deltaP = 4(surfacetension)/r. The smaller the bubble the higher the interior pressure. So if you have agitation producing a fine grained foam, when that foam fills up the vessel the pressure will go up.
Have you tried adding an antifoam? For fermentations we use corn oil or a silicone oil antifoam. A single drop of the silicone stuff can take down several liters of foam in seconds. I have also heard of mechanical foam breakers for fermentations, that spin in the air space above the liquid and break up the bubbles, but I've never used one.