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.
Thank you for the thought-out response.
It doesn't sound like site soreness, and if you're using insulin needles, those are too small to get into the muscle anyway.
Your dose might be a little high, but I doubt it's so high that it's putting you at a risk for blood clots.
It honestly sounds like it could just be soreness from exercising more if you started doing that around the same time as injections, and your body isn't used to it. It could also be an electrolyte imbalance, as some others mentioned, but if you're young and relatively healthy that's fairly unlikely.
I usually start with the most likely scenario and move from there. It's pretty unlikely to be a DVT, injection site soreness, or electrolyte imbalance, so it's likely just soreness. If you aren't already, try adding some light stretching before or after you exercise. Applying heat should help, too, if it's just muscle soreness. I would bring all this up with your doctor so they are able to rule out the more serious stuff, but I would not be overly concerned about it.
On a somewhat related note, when looking up medical information I would stick with Mayo Clinic or Cleveland Clinic for general medical stuff. For trans specific info, Fenway Health is the gold standard (imo), someone linked to them in a different response. You can also check WPATH standards of care 8, but that's meant as more of a reference for medical professionals and it might be a bit dense.
Please let us know how it goes, and keep asking questions! It's best to get from medical professionals, but sadly folks like us don't always have that luxury.