Tools for modelling and visualizing growth of cells
If the scenario is simpler, and you can't find anything by searching, I would consider just writing your own.

The modelling can be done in any language but if compute time is an issue - for example you want to run a simulation with many cells or many simulations - then I would use a language that can support that such as Julia or NumPy in Python. In fact Julia is a nice language for this type of thing as you end up with readable code that runs fast.

For visualisation in Julia specifically you could use the animation functionality of Plots.jl, which is basic but there, or could try Makie.jl. See the Molly.jl documentation for some examples of visualising particle-type processes using Plots.jl.