Tamoxifen only works against breast bud/gland growth and any pain/sensitivity too, called Gynecomastia and Mastodynia.
It will stop further growth and pain, and over time will reverse recent growth back to 1 year ago max, but most effectively anything in the previous month or so. Growth older than a year will have significant ligament support which Tamoxofen won't have any impact on. It has around a 70% success rate, so it doesn't work for everyone, although it might be the dose is inadequate in some cases (many find the NICE guideline dose is too small).
Tamoxifen will have no impact on breast fat growth (moobs), sometimes called Psudogynecomastia, and not painful/ultra sensitive.
You will be able to feel if there is breast gland growth or not (or a breast clinic with ultrasound can tell). Gynecomastia is most common in the case of taking only bicalutamide for longer than 2 months, but it can happen on hormone injections too. As we've discussed here, it can also happen for a few months after you get your testosterone back after finishing hormone therapy injections (that might be a year or more after the last injection runs out).
Tamoxifen would be contraindicated in the case of any history or high risk of DVT, and heart conditions. It has a risk of side effects of it's own, including liver toxicity and hair loss, although less likely at the lower doses used for Gynecomastia. If you're on it, probably a good idea to ask for full blood counts and liver function test after 3 months or so, to make sure your liver is coping OK.
20mg Tamoxifen tablets are very cheap, so not a significant cost issue for the NHS (other sizes are much more expensive).