Absolutely normal. Think about it from an evolutionary perspective. Tiny babies content to be put down, alone? Far more likely to starve/be eaten etc. Those that are only happy being attached to their source of heat, food and comfort? More likely to survive.

If you're happy to sit and cuddle your baby - go for it! That's far more important at this point than housework etc.
If you want to do both, try a carrier of some kind.
If you want some time without a baby attached to you, there are some great suggestions above

You're doing great!