Is HSG necessary if issue is anovulation?

Hi ladies,
I am seeing an REI because I do not ovulate regularly and my husband and I are trying for our second. I conceived my daughter on the second cycle of clomid, but at the time I was seeing a new OB/GYN and after speaking with other ladies who used clomid, it sounds like she didn't monitor me appropriately. So, I decided to see an REI with more experience. 
My GP took my progesterone levels for 2 months and determined I didn't ovulate, and the third month (this month) OPKs didn't pick up the LH surge so it looks like 3 months without O. It sounds like it would be simple for the REI to put me back on clomid or another ovulation stimulation medication, but she is also ordering an HSG
I have no problem doing all of the blood work and ultrasound she ordered, but the HSG is much more invasive and on top of it, it costs $2500. I was floored when they told me that. I told her I don't want to do it unless she has reason to believe it's necessary, and if it's clear that I'm not ovulating, then is it? Can't we just go on clomid again, and do an HSG if we are not successful and there may be another issue? Hoping someone else has had this experience and maybe thought the same thing. Thanks for any input!