Help with running base

I swim 3600m in the morning. Ride 60m on the bike. and can run 1 mile before the pain in my shins starts and by the end of it my HR is hovering around 164(around AT). So I know where my weak link is. My question…

Can I continue to build base while trying to teach my clyde body to run. Or by running at or near AT am I not getting base miles in and throwing my training off track?
Come on running make me go faster.