Hello and welcome to Healthcare Magic. Thanks for your query.
There are various forms of birth control available. Each method has its own plus and minus points. If you do not want to use condoms, there are other options like IUDs, 
oral contraceptive pills, etc. You can take your wife to a gynecologist and discuss about the different options.
If you want to check your 
sperm count, then you need to have a 
semen analysis. You can contact your doctor to order for this test. Regarding 
premature ejaculation, this can be due to a number of causes. So, the first and most important step in management of this problem is proper evaluation. This will include a detailed medical, sexual, personal and social history, a thorough physical examination and certain investigations, as per the necessity. Only if the cause is identified correctly, appropriate treatment can be given. Very often the cause is due to excessive 
anxiety and fear regarding sexual performance (what is called "performance anxiety").
So, I would advise you to see a 
psychiatrist in your place for a detailed evaluation and further treatment. Treatment will involve 
sexual counselling and in some cases, medication can also be helpful.
Wish you all the best.
Regards,
Dr. Jonas Sundarakumar
Consultant Psychiatrist