Where exactly in the thigh are you injecting? Are the spasms happening in the muscles near the injection site (i.e. are they localized), or are injections in one place on the thigh while spasms are happening elsewhere like in the calves for example?

Hitting nerves can cause spasms like that, but if you are selecting the recommended sites and using a short-enough needle (like half inch), you shouldn't be hitting nerves. I have had a physical therapist use needles to force muscles to spasm, it can be really uncomfortable and the spasms happen while the needle is in the muscle bed, so you would be able to tell (and it sounds like this isn't happening).

Here is an injection guide that shows sites for injecting subq in the thigh, to check against: PDF link, Archive.org PDF link.

I used to inject in the thighs, but I found my abdomen had more fat and was less vascular than my thighs, so it has become a preferred injection site for me. You might experiment and just see if injecting in the abdomen makes any difference.

If you really think it is vasodilation, you could get a blood pressure monitor and use it at home and keep a log (common recommendation is take a reading once in the morning and once in the evening; taking a bath, stress, exercise, and other things can influence blood pressure and throw off readings). Having a log would give you something more concrete to present to your doctor. Keeping track of changes to medication in that log would also be helpful.

I would try drinking more water and including some electrolytes with that water (there are sport electrolyte tablets you can put in water, but vitamin packets like emergen-c also often have electrolytes; you can also just use some table salt for the sodium).

You can also try incorporating more potassium rich foods in your diet like bananas, cooked spinach, sweet potatoes, button mushrooms, broccoli, etc. I used to get spasms like this ~~before bed~~ late at night in bed and often it was a combination of dehydration and not replenishing electrolytes after too much exercise.

You might add to your blood pressure log changes in diet and a report about your spasms. Collecting all that information may seem like a lot at first, but it may be clarifying such that you identify and solve the problem and don't need to keep track anymore.

I sometimes have trouble staying hydrated through the day, but I find if I carry a water bottle with me everywhere I am more likely to drink enough water.

Also remember to drink lots of water with your meals, as digestion takes a lot of water (and if you are eating like the average person, you probably aren't getting enough water from your food, so incorporating more fruits and vegetables can help keep you hydrated as well - think cucumbers, tomatoes, berries, watermelon, lettuce, etc.; this lowers the burden of how much extra water you need to drink with a meal).

I am not finding much about estrogen causing vasodilation just searching around, but I am super curious if you find something on that. Would also like to hear updates as you have them. Hope you figure it out and resolve the spasms!!