Are you under the care of a Women's Health Physio who could advise you?
I had a 3c tear 22 weeks ago. I healed well with no complications - recent endoanal scan has confirmed all is as it should be at this stage. I've been seeing a Women's Health Physio since 5 weeks post natally. I'm a very keen cyclist and road race, so as you can imagine wanted to get back training ASAP (I kept going throughout my pregnancy). Under the guidance of my Physio I was back on my bike at 4 weeks, but under strict instructions not to push myself, stick to flat riding and build up time slowly... then start building intensity. Nearly 6 months down the line I'm only just at a point where I can get away with climbing, sprinting and hard efforts. When I say 'get away with' I mean I don't have a drastic increase in symptoms - that 'heavy' feeling, urine leakage, farting and pooh leakage!!! This is doing a sport which doesn't impact on the pelvic floor like running does. It's worth noting that thanks to the input of my Physio I've been doing a full on pelvic floor exercise programme which has included bio-feedback, stimulation and muscular release in addition to standard pelvic floor exercises. I do like to go for an occasional run and I've missed that... so asked my Physio today if she thought I could give it a try, she said no immediately. She felt it'd put unnecessary impact and stress on my still recovering pelvic floor, not to mention slowing my recovery.
Even with all this taylored input to get me back to normal I'm still leaking small amounts of urine most days. Very occasionally I don't make it to the loo on time to pooh. It is still early days though - muscle takes approximately 3 months to heal and then another 3 months (with exercise) to return to normal strength.
Given it sounds like we are in a similar boat birth injury and exercise addiction wise 10 weeks for running sounds very very soon. Even with no tearing the core and pelvic floor still take a hammering during pregnancy and birth and take time and specific exercise to recover.
Could you do an alternative which wouldn't stress/ impact your pelvic floor to get your HR up like swimming or cycling? At least you'll get that endorphin fix but won't compromise recovery.