did you had a heart-to-heart conversation with him about having fertility checks? it is best that you try to see if he is in good mood or do some proper timing where he is not pre-occupied with some other things.

maybe he was just afraid to know who among two of you is infertile. let's face the fact, man are very defensive on that matter and we don't want them to feel like so small.

this would be just my suggestion. it is better if you would seek her parent's advice. ask her mom or dad to help you out brought up this issue to him.

get him into a deep conversation. asked him for a dinner outside where there could be only YOU and HIM and try to get his attention into something intimate. explain to him that this is not only for your own sake but would benefit the both of you.

you have to start the conversation by asking him politely why doesn't he wants to go.

if he doesn't want to go personally to a doctor's office, you can ask a doctor to have private collection of sperm sample at home or bring the sample to the doctor's office.