I can only provide an answer here to the "furthest" part of the question, but I hope it acts a good starting point to build upon. As far as I am aware, there are no 'journal'-like accounts of travelling the Nile, only snippets and secondary descriptions of them.

The farthest plausible Roman expeditions towards the source of the Nile occurred under Nero, from 62 CE to 67 CE, though here are no surviving first hand accounts of the supposedly farthest expeditions.

The written accounts of how far any official expedition actually went down the Nile claims that a series of expeditions organised by Nero went as far south as Meroe and beyond (Plin. NH, 6.35), from Seneca we learn of an earlier expedition that implies the expeditionary force travelled further south into modern Sudan (Sen. QN. 6.8) to somewhere believed to be around the city of Sudd (Kirwan, 1957), though there is a large amount of speculation about this. Of these accounts, only Seneca paraphrases the tales of the expeditionary group, from whom he claims to have heard from two of the officers of the group. What Seneca has quoted (See sources), we can presume to be true about the issues of the Roman expedition south of the Sahara, but also highlights the issue that the "natives" were probably Kushite, on account of them being lost - it certainly does not give the impression of the Roman expedition interacting with 'locals'. Pliny's account doesn't tackle anything south of Meroe and he highlights the topographical issue of the Sahara - that it is barren. Implicitly, what the expedition concluded from their expedition was 'it's sandy, and dry, and still sandy. There is nothing of value here' and nothing more came of it - Ethiopia was not considered a worthwhile venture as they would have to deal with the long stretches of desert before reaching the foreign and difficult to navigate terrain of Ethiopia.

Supposedly, the Caesar wanted to sail as far south as he could towards where Suetonius identified as Ethiopia, though this was cut significantly shorter by the army (Suet. Lul. 52.1), and Appian claims they traversed the Nile with 400 warships (App. B.Civ. 2.90). These are very tenuous and vague mentions of the Nile cruise, yet they are the earliest two mentions of the voyage - both written 150 years after the fact. If we were to believe both to be true, the task would be physically impossible due to the cataracts south of Meroe.

Pliny is probably our best source for ideas around the Nile, as he covers a lot in regards to wildlife and general geography, however, his account is not a journal of travelling from the delta to anywhere inland.

Sources:

Primary:

Appian, The Civil Wars. Translation can be found here

Pliny the Elder, Natural History. Translation can be found here.

Seneca the Younger, Natural Questions. Cant find a full translation online (free), but here is the relevant excerpt: Book 6, 8.4

“After many days,” so they said, “we came to huge swamps, the way out of which neither the natives knew nor could anyone hope to know; the vegetation was so entangled in water and the water impassable on foot or by boat, because the muddy overgrown marsh does not support anything except a small boat large enough for only one man. There,” he said, “we saw two rocks from which a great quantity of river-water fell.”

But whether that is the source of the Nile or only an addition to it, whether it is born there or merely returns to the surface from an earlier passage underground—do you not think that, whatever the reason, the water ascends from a great lake under the earth? For it must be that the earth has moisture scattered in many places and collected in the depths so as to be able to disgorge it with such violence.

Suetonius, Twelve Caesars. Translation can be found here

Secondary:

Kirwan, L. P. (1957), 'Rome Beyond the Southern Egyptian Fronteir' in The Geographical Journal, vol. 123 (1), pp. 13-19