Congratulations on your baby and I'm glad you're healing very well. Really, your HV and Dr. should have given you guidelines on this but given that they haven't I'm glad that you haven't leapt back into the free weights and cardio just yet.
Healing well after a c-section can be a bit misleading as it can lead you to do things sooner than you should. The advice on exercise following a c-section is refrain until after 12 weeks. You can do lots of walking in that time, which is excellent for building up your strength, but the key issue is to allow all your muscles to heal. With every pregnancy, your rectus abdominus (the band of muscle that wraps around your abdomen and joins in the middle - giving you the vertical line in your abs if you're fit - separate and, post birth, you have to allow them to come back. Post caesarean this takes about 12 weeks. LOnger than if you've had a vaginal delivery (takes around 6 weeks) as the muscles are slower to move and heal due to the cutting and stitching from the caesarean.
It's a bore and when you (outwardly) feel fine it can be really tempting to throw yourself into your pre-baby exercise regime. It's very hard when you're used to being fit to sit it out for another 12 weeks. However, in those 12 weeks post-birth you're still healing (even though you feel fine) and your abdominals will still be coming together. If you over exert you can arrest the abdominals - they'll simply grind to a halt, which will leave you with a weaker stomach and the potential for lots of issues with posture, back pain, continence further down the line.
Before having my twins I was a big runner and was used to doing loads of exercise so having to do nothing was a killer. I was also on bed rest for the last month of my pregnancy, which was dire. However, I waited the twelve weeks and I'm really glad I did. My rectus abdominus is fully joined again and my stomach muscles are back to normal (albeit slightly weaker due to the internal scar tissue).
I did lots of walking and lots of stretching during those 12 weeks and it was fine. Hard not to leap out of the door and go for a run at 10 weeks but I'm glad I waited as I'm much stronger for it now.
HOpe this helps.
Kx