Is an HSG (dye) test necessary to check cervix?

I am in my early 30s, went to an RE doctor to get IUI. I've never tried to get pregnant, so I don't think I am infertile or have fertility problems (bugs me that they list that in my paperwork just because I want to get pregnant with donor sperm). I have to pay for EVERYTHING in cash out of my pocket. You'd think it'd cost a few hundred or a thousand just to have the doctor shoot up the sperm, but it's coming to $5,000 with all the tests - one lab test after another and all the ultrasounds at over $300 a pop and now I am dreading having to have an xray done on my reproductive organs and have radioactive dyes injected to check them out. It scares me to touch them when I have no known medical problems and the cost on top of it. Can't he just try to impregnate me and if it doesn't work then go into all this? Or is it no big deal and everyone gets it done (remember I don't have insurance so if it was free maybe I wouldn't be stressing as much but still uneasy about the whole thing putting dyes in there, maybe that's what causes infertility considering women who just have at a young age can get pregnant but if you go to get treatment and they poke and prod and put the chemicals in it takes a long time). Thoughts?