Can you TTC in same cycle as HSG or HyCoSy?

Anna
Hi, in posting from London, U.K. Im a 33 (soon to be 34) year old and really struggling after 2 years of TTC and suffering a MC in January at 9 weeks with twins. My husband and I are not facing the agonising decision as to when we decide to go for treatment to help us get pregnant again quicker as the thought of waiting another year or two or more is just gut wrenching. We've had all the blood work, an internal scan on me and his semen analysis done and all seems to look ok, so far! Nothing obviously wrong But still no explaination for why it's taking its time or why we lost our beautiful twins :-( So we now face the last test (and the one we have to have to be put forward for <a href="https://glowing.com/glow-fertility-program">IUI</a> or <a href="https://glowing.com/glow-fertility-program">IVF</a>) the tubes patency test. My consultant suggested an HSG however I have today found out about the HyCoSY test and that it also tests for blockages in your tubes. Can anyone tell me if one is better than the other and also if you are able to still try to conceive in the same cycle as having the either of these tubes test done? My consultant says we should wait for one cycle but with my cycles being 35/38 days, this would feel like a lifetime. Many forums say lots of women had the dye test and tried and fell pregnant. I am so confused and don't know what's best? Or how much harm (if any?!) it would be if we continues to try and fell pregnant in the same cycle as the tubes test. Has anyone has some good medical advice that they can share on this at all? 
Thanks so much 
Anna