can your Dr really say no to you getting a fertility test done due to age??

Alright. Here goes nothing... I am 21. Please do not place judgement on me for whatever you end up reading.  My boyfriend of 4+ years on and off a few times, are TTC. We've been trying the last 3-4 months. Went off birth control, started taking pre-pregnancy First Response gummies, preseed lube, etc. Back story for this is, I have had Chlamydia twice. Two separate occasions- from the same person during a break that my boyfriend and I ended up having. Neither time did I end up having it for very long. The first time I was exposed- I had symptoms to a point where I was in the hospital only 3 days later. Second time- I obviously didn't trust him due to the first time so each time I went in right away and got it taken care of quickly. Yes. Mistake the second time, that's on me.  My doctor then told me that a big thing about STDS is that they can obviously cause infertility. I also, suffer from chronic BV which does not help, and during the summer I get yeast infections constantly. My gyno told me having BV and yeast can't hurt your fertility- because it's just an overgrowth of bacteria so that aspect I'm not really worried about. I barley get symptoms anymore to be honest and I don't get a smell when I have BV, just some sharp pains every now and again. What I'm not understanding is, when I brought up my boyfriend and I wanting to start a family, she told me I was too young and that if I wanted a kid I could come babysit hers. Now, I understand that 21 is not an "ideal" age for TTC. I get that others would wait till their late 20s but for me and my circumstances I would rather have a child earlier vs. later. Well, since she brought up the infertility part, and since we've been trying these last few months I've been thinking maybe this is due to the Chlamydia. Maybe it could've caused infertility since she said every female is different and since I had such drastic pain the first time.. it just all made sense and could possibly add up.  well when going in for my usual check up today I asked her if I would be able to get one of those ultra sounds done to test my fertility. The one with the dye, where they send it through your tubes to make sure things can be properly passed through them. She said, that in order for her to write out a script for it my boyfriend and I would have needed to try to conceive for over a year which means having sex every other day for a year.. and she always seems to trace back to my age and that I shouldn't want a kid at this point in time. I have a feeling that she may be using my age as a main factor in this but with her being my doctor shouldn't we have at least been able to talk this out?? She also said that after the test is done, that your chances of pregnancy sky rocket the next three months after getting the test done.. I'm wondering what your guys opinions are on this whole ordeal .. please refrain from judgemental comments due to my age. I'm so beyond sick of the judgment against that. I'm not 16 TTC. If I am infertile and it's something that could be worked on or treated such as PID, or this dye test-- is it wrong of me to want to get it all figured out when I'm young?? Feedback appreciated.