It is possible to do word searches in pdf copies of Complete Peerage and Complete Baronetage. Below is a list of Baronets who are called "physicians" in the Baronetage. Probably similiar searches could be done for "dentist", etc.
(Note: since this comes from Complete Baronetage, it covers Baronetal titles created through 1800. Later creations are not included, but similar searches could probably be done in Burke's and Debrett's.)
1. Sir Henry Holland, 1st Bt.
2. Sir Henry Middleton, probably 7th Bt. (d.1759)
3. Sir James Stonhouse, 10th & 7th Bt., was a physician as well as a clergyman.
4. Sir Benjamin Kemp, 7th Bt.
5. Sir George Hampson, 4th Bt.
6. Sir Edward Greaves or Graves, 1st Bt. Complete Baronetage says that he was the first physician ever given an hereditary title in recognition of such a role.
7. Sir Alexander Douglas, 7th Bt., of the 1625 creation.
8. Sir John Moncreiff, 5th Bt.
9. Sir George Duncan Gibb, who might have been 7th Bt., but never assumed the title
10. Sir James Hay, 4th Bt., of the 1635 creation.
11. Sir George Wakeman, 1st Bt.
12. Sir Thomas Williams, 1st Bt. (1674 creation)
13. Sir Thomas Archer Colt, 7th Bt.
14. Sir Alexander Fraser, 1st Bt. (1673 creation)
15. Sir Robert Cuningham, 1st Bt. (1673 creation)
16. Sir Alexander Bannerman, 6th Bt.
17. Sir William Sinclair, 2nd Bt. (1704 creation) seems to have been a Baptist preacher as well as a physician
18. Sir Alexander Dick, 3rd Bt.
19. Sir Hans Sloane, Bt.
20. Sir Edward Hulse, 1st Bt.
21. Sir Edward Wilmot, 1st Bt. (1759 creation)
22. Sir William Duncan, Bt. (1764 creation)
23. Sir John Pringle, Bt. (1766 creation)
24. Sir Clifton Wintringham, Bt.
25. Sir George Baker, Bt.
26. Sir John Elliott, Bt. (1778 creation)
27. Sir Richard Jebb, Bt.
28. Sir Lucas Pepys, 1st Bt.
29. Sir Hugh Reeve Beevor, 5th Bt.
30. Sir Walter Farquhar, Bt. (1796 creation)
31. Sir John Macnamara Hayes, Bt.
32. Sir Francis Milman, Bt.
33. Sir Thomas Molyneux, 1st Bt. (1730 creation)
34. Sir William Blunden, 4th Bt.
35. Sir Edward Barry, Bt.; and his son:
36. Sir Nathaniel Barry, 2nd Bt.
37. Sir George Leonard Staunton, Bt.