Mazal tov on the birth of your son!

Once a married woman has finished shivah neki'im there is no need for her to do any further bedikot even if she needs to delay going to the mikveh. This is true until the time of the month that she would expect her next period. In your case, since a woman after childbirth is assumed halachically not to be expecting a period for a long time, you can rely on your shivah neki'im without needing any more bedikot even though you are not going to the mikveh for a while.

However, while it is true that most physicians feel that relations should be medically avoided for six weeks (and until after a post-partum checkup) many doctors allow bathing and going to the mikveh well before that. Furthermore, you can do your preparation with a shower rather than a bath as long as you are careful to wash your entire body, prepare at home to prevent infection from other women and ask to be the first woman to immerse after the mikveh water is changed. This will markedly minimize the chance of infection. It is sufficient to immerse twice, once before and once after the bracha, even if your minhag is usually to immerse more than that.

Explain to your physician that for mikveh immersion you will not be sitting in the bath but dunking twice in clean water for less than a minute. If you can get permission from your doctor, you can consider going to the mikveh to allow physical contact between you and your husband even if relations would still be off limits.