I always inject T into my behind but the last time I did my shot it hurt while I was injecting it which is a bit odd for me. Not necessarily pain but more discomfort. After pulling out the syringe I noticed some bleeding and as I went to grab a tissue it started to squirt out and all down the back of my pants and onto the ground. This has happened before but not quite as bad, as in it didn't bleed this much; on a good day it does't bleed at all. Has this happened to anyone else? I know some people pull back the plunger slightly to prevent this, should I consider doing this?

Anytime you break the skin there is a chance of bleeding.

I'm diabetic and take insulin.  Every so often I strike oil (blood) and my needle is only 3/16".  It happens.

Ask a nurse or your endo's staff the next time you see them. There are different angles for sticking needles into the body for different purposes.
I haven't even started seeing my therapist yet so I have no experience with HRT. However questions I would ask are:
Where is this supposed to be injected? (Into fat, muscle, vein, or artery? This affects the angle of the needle you should use in relation to the body part. A nurse or quick look up online can show you the difference)
How thick is this stuff and what size and type of needle is recommended? (I'm pretty sure you don't want to use a lumbar puncture needle for this so be sure that you've got good equipment for this)
How deep are you supposed to stick yourself? (This isn't an atropine emergency so if its not recommended to stab yourself with the hub of the syringe spending quality time with your then why do that? You'll just increase the risk of bleeding and infiltration)
What portion of the body part are you supposed to stick? (Seriously there's a lot of real estate when it comes to the human body in comparison to a needle and its cargo so be sure of what's a good spot)

That should help.