It's possible (if you don't mind the results to be a bit stale, they're updated every Sunday morning) with a SEDE query. You'll need your network account ID, which you can find in the URL shown in your address bar when you visit https://stackexchange.com/users/current. For example, when I search for my own posts (account ID 6085540) and the word 'company', these are the results:

Of course, Google's search and Stack Exchange own (Elastic)Search are a bit smarter, as they can correct spelling errors, and search for plurals and multiple keywords.
For reference, here is the complete query (feel free to fork it if you want to play around):
-- result table, don't rename and keep the site column
create table #results (site nvarchar(250), type nvarchar(10), id int, title nvarchar(250),
creationdate datetime, score int);
declare @sql nvarchar(max) = '' -- holds build up sql string
-- build one biq union sql, for each db
select @sql = @sql
+ iif( len(@sql) > 1
, 'union'
, 'insert into #results'
) +
-- here goes the per site query, fully qualify the database objects
N'
select ''' + name + '''
, ''Answer'', a.id, q.title, a.creationdate, a.score
from ' + quotename(name) + '.dbo.posts as a
inner join ' + quotename(name) + '.dbo.posts as q on a.parentid = q.id
inner join ' + quotename(name) + '.dbo.users as u on a.owneruserid = u.id
where u.accountid = ' + CAST(##AccountId:int## AS nvarchar) + '
and a.body LIKE ''%' + ##keyword:string## + '%'''
+
'union' +
N'
select ''' + name + '''
, ''Question'', q.id, q.title, q.creationdate, q.score
from ' + quotename(name) + '.dbo.posts as q
inner join ' + quotename(name) + '.dbo.users as u on q.owneruserid = u.id
where u.accountid = ' + CAST(##AccountId:int## AS nvarchar) + '
and q.posttypeid = 1
and q.body LIKE ''%' + ##keyword:string## + '%'''
from sys.databases
where database_id > 5
-- AccountId: The global account ID of the user, which you can find in the URL of their network profile. Visit this link: https://stackexchange.com/users/current to see your own ID.
-- execute it
exec (@sql)
-- show results
select
-- URL builder from Lamak http://stackoverflow.com/a/38129701
'http://'
+ case PARSENAME(site,1)
when 'audio' then 'avp'
else PARSENAME(site,1)
end
+ coalesce('.'
+ case PARSENAME(site,2)
when 'audio' then 'avp'
else PARSENAME(site,2)
end , '')
+ IIF(patindex('%.MathOverflow%',site) > 0
, ''
, coalesce('.' + PARSENAME(site,3), '')
)
+ IIF(patindex('%.MathOverflow%',site) > 0
, '.net'
, '.com'
)
+ (CASE type WHEN 'Answer' THEN '/a/' ELSE '/q/' END)
+ CAST(id AS nvarchar)
+ '|'
+ title,
type,
creationdate,
score
from #results
order by score desc
drop table #results