No it shouldn't affect your fertility in the long term.
Many people can have side affects so it's best to research about them, best way is to search in YouTube and you will find many helpful resources. It may be mood swings, head aches, change in period etc. There are many different types of pills and other types of contraception take your time and choose them wisely.
And its normal to not feel anything if the condom is thick, perhaps try a thinner or a dotted condom for better sensation.