I live in a house that is over 110 years old. We recently installed a whirlpool tub with a tub surround, but there is gaps between the tub and the surround unit. What do i use to fill in those gaps?

There should be manufacturer's recommendation for sealant in the installation instructions. But you can use silicone caulking to seal (fill-in) the gaps.

If installed properly, the surround should not leave gaps. Gaps mean your walls are either not plumbed or square and / or were not properly prepared for the installation.

When we install tub surrounds, we also use 2"x 4" braces that push each panel at the joint against the wall. Tension is released after two days. That way, all seems are tight and no additional caulking is needed.

First! Lose the caps. That's the same as yelling at us. Was your surround installed by a professional? How wide are the gaps and what's behind them?
Back to you, Tom