I have recently had a specialty placement in hands, and believe I can address this issue. You're describing potentially an intra-articular fracture of the D5 MCP level.
The general guidelines for conservative treatment (since you were put in a splint I'm assuming) are as follows:

Treatment Guidelines
Protective splinting/casting 3-6 weeks
4 wks commence gentle AROM (if stable fracture may commence out of splint)
6 wks gentle PROM, night splinting for protection, may commence gentle resisted (i.e. putty)
8 weeks before you can commence grip strength

You also mentioned that your finger has been strapped for the last 5 weeks to your ring finger to brace it and support it. Please stop this! This is called 'buddy fingering' and can actually cause more malrotation and deformity.

In terms of exercise, I would recommend doing the following exercises every 1-2 hours (except when sleeping):
-with wrist in neutral: make a fist, then straighten all your fingers
-try and touch the tip of your little finger to the tip of your thumb
-using your non-injured hand, block your little finger so only the tip can bend and straighten (i.e. the DIP joint).
-using your non-injured hand, block your little finger so the PIP & DIP joint are bending and straightening (MCP joint remains still)
-place your injured hand on a small ball or on top of your non-injured hand (because we want your injured hand to be slightly cupped so your MCP joints are slightly bent). Now straighten all your fingers (i.e. extend your MCP joints).
Repeat all these exercises 3-10 times depending on your pain tolerance.

You should be able to commence passive ROM, but as always - it is recommended you have this cleared with a physician first.

If you have a plastics physiotherapy department available where you live (in the hospital), I would recommend going there. Sometimes when you fracture your finger the way you did, it can result in a volar or dorsal dislocation, leading to further problems such as a Boutonniere or swan-neck deformity. They can also do passive joint mobilizations to improve the normal arthrokinematic movement at the MCP joint.

Cheers,
Lisa