A.Is this type of marriage accepted?
In India, especially South India, it is common for a man to marry his father's sisters daughter or mother's brother's son or daughter. The problem comes when the cousins come from father's brother's children or mother's sister's children. There should not be an issue for you as your situation would be accepted.
B.Can there be any medical issues for the next generation?
This would be a valid point that needs professional to advise. First, make a family tree from your side and the girl's side going back at least 4-5 generations. Make a note of the diseases, birth defects, stillbirths, members with extra toes or fingers, low intelligence etc. Basically, the medical specialist will look at this marriage between close relatives as Consanguineous marriage and try to predict potential congenital diseases that can be passed on by you both to your children in the future.
There are many hospitals in the corporate/private sector and the major teaching medical colleges and premier government hospitals that offer Pre-marriage Genetic screening and counseling for closely related people about to get married.
Can this marriage affect us?
Once you attend a couple of consultations with the experts, they would check for the potential risk of abnormalities with vision, hearing, mental development and certain blood disorders.If there is no serious risk of passing down diseases, then you need not worry. Both of you love each other and have a harmonious life ahead.
The advice to you would be, keep an open mind, the problems are more when it is a first-degree cousin etc, so meet the genetic counsellors in your area and then go forward with your marriage and life.
You can also read these simple brochures for some more details.