I think there must have been at least one other Alwar Imperial Service Infantry regiment and there was a cavalry regiment, based on these few gleanings:
Indian Army List, July 1919, with War Services
https://archive.org/details/in.ernet...012/page/n1427 [SEE photo below]
“Here are all the Indian units listed by CWGC - those which suffered at least one casualty in WW1. The numbers in brackets are the numbers of names in the CWGC database for each unit.
1st Brahmans (119)
1st Duke of York's Lancers (Skinner's Horse) (34)…
142nd Jodhpur Infantry, Indian States Forces (17)
145th Alwar Infantry (1)
Alwar Infantry (29)
Alwar Lancers (12)”
https://www.greatwarforum.org/topic/...rmy-regiments/