I had the same effect on injectible Test. Was ok for about a year and then like clockwork, dizziness with 12-14 hrs after injection. This was on HRT, too...so the dose was pretty small (100mg/week).
It took a visit to a very sharp doctor to catch it, but what was happening is that the Test was decreasing my thyroid function. We went over many labs and found that when injecting test (particularly right after the injection), my TSH would jump from the low 1's to the mid 3's. The range is 1.0 to 5.0, but most smart docs know that anything above 3.0 spells thyroid (hypothyroid) trouble.
I am on 3 grains/day of Armour Thyroid now and no dizziness problems to speak of.
R1