I do not think you are unusual, I think a lot of new mums feel this way. It is completely natural to feel bored, given you have probably been working outside of the home, with frequent interaction with others. Suddenly you are at home with this baby who you are entirely responsible for but who does very little beyond sleeping, crying, feeding and pooing.
The stage you are at now, is probably the last time you will get to do anything for you for a long time. If you want to get fit, now is the time. In a few months time, it will be hard to keep your little one in the buggy without them throwing a great big wobbly about it, so get those long walks in now.
Catch up with friends or make new ones, it will be a lot harder when your child always want to talk to you, or demands your attention to play.
Do not be too hard on yourself. Treat yourself, go for coffee and read a book, maybe sleep.
Get your child used to being away from you for short periods, it is invaluable that you do given there may be times when you have to be away from them, get your baby to at least take a bottle of expressed milk, you could go out for the evening with your partner then.