MySQL supports "SELECT ... FOR UPDATE" specifically for this situation to make sure the row isn't overwritten while you're processing the the row contents.
https://dev.mysql.com/doc/refman/5.7/en/innodb-locking-reads.html
The above link even gives a very similar example (except for exploding the elements, increasing the one you want, and imploding them back together).
SELECT counter_field FROM child_codes FOR UPDATE;
UPDATE child_codes SET counter_field = counter_field + 1;
The better answer, as Tim suggested, is to store this data in a separate table, especially since you have a variable number of items for each row. I don't know how you currently know that you want to update, say, the 3rd item but I'll assume that's known.
Let's say these numbers are temperature readings from various sensors at a "location" and they gradually go up and down. Your main table is "locations" with with fields:
id (int, auto-increment), location_name (varchar), ...
You're then going to create a new table called "readings" with fields:
id (int, auto-increment), location_id (int), temperature (smallint)
The "id" from the first table is going to match up to the "location_id" of many records in "readings".
When you want to add a new temperature reading to a location (I'm assuming you'll have a $location_id and $new_reading variables in PHP):
INSERT INTO readings (location_id, temperature)
VALUES ( $location_id, $new_reading )
(NOTE: You should be properly sanitizing your inputs, using PDO, or other library, but that's out of scope for this answer or I'm going to be here all night. :-) )
Let's say you want to update the 3rd reading for this location, that would mean the "offset" is 2 and you only want to update 1 record so that's what "LIMIT 2, 1" means below. (I tried and failed to find a way to do this in only 1 query; UPDATE does not seem to support offsets, at least not in my version of MySQL.)
SELECT id FROM readings WHERE location_id = 1 ORDER BY id LIMIT 2, 1;
/* Let's say you stored the above result in $reading_id */
UPDATE readings SET temperature = temperature + 1 WHERE id = $reading_id;