Estrogen does not dilate blood vessels, and vasodilation won't cause pain. It's very unlikely that the hormone is causing the pain.
I have a few questions, if you don't mind? You said you are doing the injections subcutaneous. Where are you injecting? What length of needle are you using? Subcutaneous injections are relatively painless and shouldn't be causing any of the issues you are describing, but if you're using a needle that is too big or injecting in a bad spot the pain could be related to injection site soreness.
Pain in the legs and below the knee could be a sign of deep vein thrombosis. It's very unlikely, but estrogen can make you more susceptible to blood clots. You are at higher risk for this if you smoke cigarettes (especially if you're over 35), if you have a more sedentary lifestyle, or if your serum estrogen level is too high. Subcutaneous injections tend to lead to higher serum estrogen levels, which can put you at a higher risk for blood clots.
You said you are DIY, is anyone checking your estrogen levels? What dose of estrogen are you taking, and how often?
It's pretty unlikely the pain is from a DVT, but that is a very serious complication you need to rule out (a dislodged clot from a DVT that travels to your lungs can cause a pulmonary embolism, which can potentially be fatal).
I hope this doesn't come across as condescending, but these are the questions I would ask if you were a patient.