No, injection frequency won’t change your SHBG. I’m saying that since your’s is very likely low, you would most likely need to inject daily or EOD to feel optimal. I suggest ED injections.
23 gauge??? Ouch!! That’s completely unnecessary and very old school. Just pick yourself up some insulin needles. I would suggest getting 27-29 gauge 1/2” insulin syringes. Inject into your thighs or shoulders. I’ve been using the thighs for years with good success. Have a ton of area to inject, and it’s basically painless. There’s no need to draw with one syringe, and inject with another.