Hi , How are you doing.?
This condition is called Vaginismum.
About he name of gel - it is KY Jelly or V 2 gel or Klimpass gel.
These gels can help you to improve the lubrication inside vagina , but that will not relieve her pain.
Let me explain how to manage. Any virgin , young lady will have this problem. This is not her mistake , When you try to push your penis into her vagina , unknowingly her muscles around thigh & around vaginal opening start to contract. More you try ,more is the contraction & more is the pain, it's not lack of lubrication. Once you create pain, next time she will be scared of pain & will hold tighter
You both have to spend 30-60mins in love making , called foreplay. It means by this her discharge from vagina will be more & you won't need any other lubrication, by this your penis also will be firmer. For first few days don't use your penis , instead use your one finger into her vagina & give her the pleasure, gradually over few days use 2 fingers, by doing so size of vagina gradually increases, Once she can handle 2-3 fingers,now use your penis.
Again position of sex is important. You should not be on top, you will push & will never know when she has pain.
You stand by the bed, her hip at edge of bed with pillows below. Now her pelvic bones will relax & slowly try to enter.
Other position is tell her be on top, like how she sits on Indian toilet. This position her pelvis is relaxed. Then tell her to come on to you, she will obviously not cause herself pain. Let her decide how deep she wants the penis, you just hold thighs apart to relax her muscles.
This is a very intimate & intricate topic & very difficult topic to explain. But I hope I could clear your query. Any more further query do write back.
Don't worry both of you will have a great time & life ahead
All the best
Dr.Balakrishnan