You need to ask to have the RE put in charge of your treatment. HSG only if the SA is clear? What kind of stupidity is that? You need an HSG before even touching meds. End of story. You need blood work before touching meds. That is not a point where you can waiver. How can she properly treat you without making sure there isn't a glaring issue first? Just because you ovulate doesn't mean there is an issue.
Your OB has no clue what she is doing and shouldn't be ordering any of this. It shouldn't be "well, I don't think you need blood work, but if you want it we can do it". It is an absolute must. There are pages of paperwork including family history that I had to complete for my RE appiontment- there shouldn't be any questions on history- they should have given you guidelines of exactly what information to gather.
She may be a wonderful OB and great at annuals and pregnancy/delivery, but she clearly has zero education in infertility.