Hi Harsha,
Well you have used HSRP and BGP also at you core router..now hsrp will prefer only one router at a time to select
the virtual IP...so to tackle with hsrp you need to create two hsrp group. one will be standby for other and that standby will be primary for
next group..this way you will be able push traffic upto two core router.
Now for BGP consider incoming and outgoing traffic..
for incoming traffic you need to divide your LAN IP in two parts (if it is /23 need to create two /24 pools but it it is /24 only there is limitation)
announce one /24 from one ISP and other /24 from other ISP...but don't forget to announce /24 from both ISP as a backup
for outgoing traffic if you are learning default route only i don't think it will be load shared..but if you are receiving full bgp or partial bgp you can do load
share by playing with as-path along with some regular expresion.
If you can share config details there could be more focus on solution
hope this is useful
Regards
Mahesh