I have access to a transcript for Crookham Presbyterian 1811 to 1833 (so unfortunately just outside the dates you are mainly interested in). There are quite a few Trotter baptisms, and there seems to have been more than one Henry/Hendry. These are the two Trotter baps closest in time to your period.
George s/o Hendry Trotter by his wife Jane McKensy. Born at Crookham 27 Oct 1811.
7 Feb 1813 Andrew s/o Hendry Trotter, Mason, by his wife Margret Hunter. Born at Bruce's Castle, Ford Parish 4 Feb 1813.
Just in case it is of interest, there was this bap in Wooler West Presbyterian:
15 Jan 1767 Elisabeth daughter to James Troter (sic) by his wife Bella, Wooller.
I agree with the suggestion that your family may have been baptised outside Crookham even if they lived there as the particular denomination and also the particular Minister were generally very important to dissenting families and they were prepared to lug a baby a reasonable distance to get to the Minister/church of their choice. That includes over the Border.
Records of dissenting congregations in Northumberland are also incomplete - some Ministers kept no records even into the 19th century and some registers were damaged or lost. There were calls for some kind of civil registration long before 1837 because of these kinds of problems.
BTW, I think the wording of the restriction when you try to access the images on-line is misleading as I have been informed by FamilySearch that non-LDS members cannot access these images even at a Family History Centre.
I pursued this with Familysearch a couple of years ago, as I have an LDS account (for members of the public) to order films but was still not able to access some Northumberland images even at my local LDS Family History Centre.
After a couple of weeks of persistent email enquiries to answer-bots I was eventually escalated to a real human, and then handed rapidly up the hierarchy of expertise as no-one could work out why I could not access the records when they could. It turned that the owner of the records (i.e. the Northumberland Archives) had placed restrictions so that only LDS church members with an LDS member account are able to view the records. Presumably this is to reserve the ability to on-sell the records to a commercial outfit at some point...but still waiting for that to happen.
