Girlfriend wants to have sex without condom but I’m not comfortable with having unprotected sex?

use a condom but poke holes in it and dont tell her 

You are correct that you are entitled to use a condom.

It does take some time for new hormonal contraception to take effect and she may not be fully covered as yet.

You then need to BOTH attend a sexual health clinic and be screened for disease.

You also need to be confident you are BOTH treating this as an exclusive relationship.

At that point you can reassess the need for condoms.

There is little difference in the sensation for most women (with/without condom) so it is an unusual request on her part unless she is wanting you to enjoy sex more but you will only do so if you are comfortable not using a condom.

If you aren't comfortable don't do it, STD should be low risk if you are both tested but no contraception is 100% and if you want to double that up then thats your choice.

She should be on birth control and (you didn't say what the shot was for if it's for birth control make sure she's getting the shot when she's supposed to) both of you should get tested for stds, before you decide not to use condoms. You should also be faith full to each other. If either of you have had sex with previous partners (or your not monogamous partners) and you didn't know their std status, you could be infected with an std. 

Where did she get that idea? I can tell you that it doesn't feel much different to a woman whether a condom is used or not. There are very few nerve endings in the vagina, and the stimulation a women gets is not inside the vagina, but from pressure on the clitoris. She's the one who needs to get tested, although it would be good if both of you were. Then it would be safe, as long as you're both monogamous. 

If she’s on birth control, the risk of pregnancy is very low. Just make sure she gets her shots on time. If you’re in a monogamous relationship, and you trust her, it’s probably fine to stop using condoms. But if you feel more comfortable using them, then just keep doing that. It’s nice to see a man that’s responsible about using protection. From my experience, most guys only use them if the woman insists on it. Then they get upset when she ends up pregnant. You’re definitely smart for taking responsibility for yourself. But you should have this discussion with HER. There may be a reason why she wants to stop using condoms. They can cause pain and irritation for some women.