If you are on Bicalutamide for more than 2 months, you should have been offered low dose Tamoxifen to take with it, 1 or 2 x 20mg/week. (You'll probably need to start on the higher dose for a month, since it should have been started with the Bicalutamide and takes time to build up to the working level. When starting out, you may find the tablets only give relief for a short time, and snapping them to take smaller doses more frequently might help with this, but that will resolve when you've built up the working dose in your system.) This prevents the breast gland pain (mastodynia) and growth (gynecomastia). It can reverse recent breast gland growth, but not anything long-standing.
(This does not apply to taking bicalutamide with injections or Relugolix.)
There are some medical conditions where you can't take it, e.g. history of DVT. Get your GP to check liver function after you've been on Tamoxifen for 3 months to make sure your liver is coping with it.
Breast gland pain and growth can happen on other hormone therapy medications too, but it's rarer, and in those cases, Tamoxifen is only provided if/when it happens. However, it's pretty inevitable when taking Bicalutamide alone, and I would say it should be prescribed with the Bicalutamide, but I know it often isn't.
Tamoxifen will not help with breast fat growth (which is painless), only breast gland growth (which is often painful).
Dizziness is a side effect of Bicalutamide, but not a common one. You could ask to switch to Relugolix or one of the hormone therapy injections, but having already got the breast gland pain, you will probably need the Tamoxifen anyway. If switching to injections, you should overlap with the Bicalutamide for a couple of weeks (not necessary if switching to Relugolix).