Ruta Grav 30 C may help, as it is known to help in joint and musculoskeletal issues. The dose is 2 globules three times a day. But there are no double blind randomized controlled trial of benefit of Ruta Grav in tennis elbow or trigger thumb, specifically. There are anecdotal evidence of it's benefit in musculoskeletal / joint disorders. So you may take it with the other measures too.
Following are the comprehensive measures for tennis elbow;
1) Anti-inflammatory analgesics like Ibuprofen for around 10-14 days.
2) Elbow brace
3) Physical therapy
4) Warm compresses
5) Local analgesic patch / ointment / spray
These are the initial modalities and if the pain does not respond than the further interventions would be required;
1) iontophoresis, phonophoresis
2) electrical stimulation
3) shock wave therapy
4) local steroid shots
The specialist to handle both the conditions is physical medicine and rehabilitation specialist. Most of the above modalities are done at physiotherapy center.
Trigger thumb occurs due to degeneration of the tendon of the thumb and prevents its smooth movement in its covering (sheath). It develops more frequently in individuals with diabetes, thyroid disorders and in patients with osteoarthritis. This may also be associated with inflammatory arthritis, gout, or chronic infection.
1) oral nonsteroidal anti-inflammatory drugs,
2) steroid injection, and
3) splint that prevents motion of the joints of the thumb.
If these are not effective; surgery may be needed.
Please feel free for your follow up questions.
I would be happy to assist you further, if you need any more information.